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Tytuł:
Lipschitz differences and Lipschitz functions
Autorzy:
Balcerzak, Marek
Buczolich, Zoltán
Laczkovich, Miklós
Powiązania:
https://bibliotekanauki.pl/articles/966671.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Lipschitz function
circle group
difference function
Źródło:
Colloquium Mathematicum; 1997, 72, 2; 319-324
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Averages of uniformly continuous retractions
Autorzy:
Jiménez-Vargas, A.
Mena-Jurado, J.
Nahum, R.
Navarro-Pascual, J.
Powiązania:
https://bibliotekanauki.pl/articles/1217171.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
uniformly retraction
Lipschitz retraction
extreme point
Opis:
Let X be an infinite-dimensional complex normed space, and let B and S be its closed unit ball and unit sphere, respectively. We prove that the identity map on B can be expressed as an average of three uniformly retractions of B onto S. Moreover, for every 0≤ r < 1, the three retractions are Lipschitz on rB. We also show that a stronger version where the retractions are required to be Lipschitz does not hold.
Źródło:
Studia Mathematica; 1999, 135, 1; 75-81
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A survey on Lipschitz-free Banach Spaces
Autorzy:
Godefroy, Gilles
Powiązania:
https://bibliotekanauki.pl/articles/746348.pdf
Data publikacji:
2015
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Lipschitz maps
geometry of Banach spaces
Opis:
This article is a survey of Lipschitz\dywiz free Banach spaces and recent progress in the understanding of their structure. The results we present have been obtained in the last fifteen years (and quite often in the last five years). We give a self\dywiz contained presentation of the basic properties of Lipschitz\dywiz free Banach spaces and investigate some specific topics: non-linear transfer of asymptotic smoothness, approximation properties, norm\dywiz attainment. Section 5 consists mainly of unpublished results. A list of open problems with comentary is provided.
Źródło:
Commentationes Mathematicae; 2015, 55, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized trend constants of Lipschitz mappings
Autorzy:
Szczepanik, Mariusz
Powiązania:
https://bibliotekanauki.pl/articles/747268.pdf
Data publikacji:
2018
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Banach space
Lipschitz mapping
fixed point
Opis:
In 2015, Goebel and Bolibok defined the initial trend coefficient of a mapping and the class of initially nonexpansive mappings. They proved that the fixed point property for nonexpansive mappings implies the fixed point property for initially nonexpansive mappings. We generalize the above concepts and prove an analogous fixed point theorem. We also study the initial trend coefficient more deeply.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2018, 72, 2
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On lower Lipschitz continuity of minimal points
Autorzy:
Bednarczuk, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/729359.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
minimal points
Lipschitz continuity
vector optimization
Opis:
In this paper we investigate the lower Lipschitz continuity of minimal points of an arbitrary set A depending upon a parameter u . Our results are formulated with the help of the modulus of minimality. The crucial requirement which allows us to derive sufficient conditions for lower Lipschitz continuity of minimal points is that the modulus of minimality is at least linear. The obtained results can be directly applied to stability analysis of vector optimization problems.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2000, 20, 2; 245-255
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the state estimation for nonlinear continuous-time fuzzy systems
Autorzy:
Delmotte, Francois
Hammami, Mohamed Ali
Rettab, Nour El Houda
Powiązania:
https://bibliotekanauki.pl/articles/2106502.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fuzzy systems
Lipschitz analysis
observer design
Opis:
A large class of nonlinear systems can be represented or well approximated by Takagi-Sugeno (TS) fuzzy models, which in theory can approximate a general nonlinear system to an arbitrary degree of accuracy. The TS fuzzy model consists of a fuzzy rule base. The rule antecedents partition a given subspace of the model variables into fuzzy regions, while the consequent of each rule is usually a linear or affine model, valid locally in the corresponding region. In this paper, the observer design problem for a T-S fuzzy system subject to Lypschitz perturbation is investigated. First, an observer of Kalman type is designed to estimate the unknown system states. Then, the class of one-sided Lipschitz for a TS fuzzy system subject to a sufficient condition on the bound is studied. The challenges are discussed and some analysis oriented tools are provided. An example is given to show the applicability of the main result.
Źródło:
Archives of Control Sciences; 2022, 32, 1; 57--72
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the theorem of Filippov-Pliś and some applications
Autorzy:
Donchev, T.
Farkhi, E.
Powiązania:
https://bibliotekanauki.pl/articles/970906.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
differential inclusions
one-sided
Lipschitz
Filippov
Plis
Opis:
In the paper some known and new extensions of the famous theorem of Filippov (1967) and a theorem of Plis (1965) for differential inclusions are presented. We replace the Lipschitz condition on the set-valued map in the right-hand side by a weaker onesided Lipschitz (OSL), one-sided Kamke (OSK) or a continuity-like condition (CLC). We prove new Filippov-type theorems for singularly perturbed and evolution inclusions with OSL right-hand sides. In the CLC case we obtain two extended theorems, one of which implies directly the relaxation theorem. We obtain also a theorem in Banach spaces for OSK multifunctions. Some applications to exponential formulae are surveyed.
Źródło:
Control and Cybernetics; 2009, 38, 4A; 1251-1271
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized directional derivatives for locally Lipschitz functions which satisfy Leibniz rule
Autorzy:
Grzybowski, J.
Pallaschke, D.
Urbański, R.
Powiązania:
https://bibliotekanauki.pl/articles/970935.pdf
Data publikacji:
2007
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
generalized directional derivatives
point derivations
Lipschitz functions
Opis:
In this paper a concept of a generalized directional derivative, which satisfies Leibniz rule is proposed for locally Lipschitz functions, defined on an open subset of a Banach space. Although Leibniz rule is of less importance for a subdifferential calculus, it is of course of some theoretical interest to know about the existence of generalized directional derivatives which satisfy Leibniz rule. The proposed concept of generalized directional derivatives is adopted from the work of D. R. Sherbert (1964) who determined all point derivations for the Banach algebra of Lipschitz functions over a complete metric space.
Źródło:
Control and Cybernetics; 2007, 36, 4; 911-924
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Point derivations for Lipschitz functions andClarkes generalized derivative
Autorzy:
Demyanov, Vladimir
Pallaschke, Diethard
Powiązania:
https://bibliotekanauki.pl/articles/1339173.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
point derivations
generalized directional derivative
Lipschitz functions
Opis:
Clarke's generalized derivative $f^0(x,v)$ is studied as a function on the Banach algebra Lip(X,d) of bounded Lipschitz functions f defined on an open subset X of a normed vector space E. For fixed $x\in X$ and fixed $v\in E$ the function $f^0(x,v)$ is continuous and sublinear in $f\in Lip(X,d)$. It is shown that all linear functionals in the support set of this continuous sublinear function satisfy Leibniz's product rule and are thus point derivations. A characterization of the support set in terms of point derivations is given.
Źródło:
Applicationes Mathematicae; 1996-1997, 24, 4; 465-474
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A special case of generalized Hölder functions
Autorzy:
Lupa, M.
Powiązania:
https://bibliotekanauki.pl/articles/122471.pdf
Data publikacji:
2014
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Lipschitz condition
generalized Hölder condition
equivalency of norms
Opis:
In this paper some properties of a special case of generalized Hölder functions, which belong to the space W γ [a, b], are considered. These functions are r-times differentiable and their r-th derivatives satisfy the generalized Hölder condition. The main result of the paper is a proof of the theorem that product of two functions belonging to the space W γ [a, b] also belongs to this space.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 4; 81-89
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On a certain property of generalized Hölder functions
Autorzy:
Lupa, M.
Powiązania:
https://bibliotekanauki.pl/articles/122720.pdf
Data publikacji:
2015
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Lipschitz condition
generalized Hölder condition
y-Hölder condition
Opis:
In this paper some properties of functions belonging to the space Wy[a,b] of generalized Hölder functions are considered. These functions are r-times differentiable and their r-th derivatives satisfy the generalized Hölder condition. The main result of the paper is a proof of the fundamental lemma that the recursive model-defined functions ℎk: I × Rk+1 → R, k = 0,1, … , r are a special form and belong to the space Wy[a,b].
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 4; 127-132
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Remarks on retracting balls on spherical caps in \(c_{0}\), \(c\), \(l^{\infty }\) spaces
Autorzy:
Goebel, Kazimierz
Powiązania:
https://bibliotekanauki.pl/articles/2078971.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Retraction
Lipschitz constant
radial projection
truncation
spherical cap
Opis:
For any infinite dimensional Banach space there exists a lipschitzian retraction of the closed unit ball B onto the unit sphere S. Lipschitz constants for such retractions are, in general, only roughly estimated. The paper is illustrative. It contains remarks, illustrations and estimates concerning optimal retractions onto spherical caps for sequence spaces with the uniform norm.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2020, 74, 1; 45-55
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the contingent of the graph of the sum of two mappings
Autorzy:
Turowska, M.
Powiązania:
https://bibliotekanauki.pl/articles/122062.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
Tematy:
mappings
graph
Lipschitz mapping
odwzorowania
graf
odwzorowanie Lipschitza
Opis:
It is shown that the graph of the sum of two Lipschitz mappings of the real line into a normed space of infinite dimension, whose graphs have tangents, need not have a tangent. Moreover, it turns out that the contingent of the graph of their linear combination may depend on the coefficients of that combination in quite "nonlinear" way.
Źródło:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2013, 18; 55-66
2450-9302
Pojawia się w:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Strong continuity of semigroup homomorphisms
Autorzy:
Basit, Bolis
Pryde, A.
Powiązania:
https://bibliotekanauki.pl/articles/1217352.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
representation
semigroup homomorphism
weak continuity
strong continuity
Lipschitz map
Opis:
Let J be an abelian topological semigroup and C a subset of a Banach space X. Let L(X) be the space of bounded linear operators on X and Lip(C) the space of Lipschitz functions ⨍: C → C. We exhibit a large class of semigroups J for which every weakly continuous semigroup homomorphism T: J → L(X) is necessarily strongly continuous. Similar results are obtained for weakly continuous homomorphisms T: J → Lip(C) and for strongly measurable homomorphisms T: J → L(X).
Źródło:
Studia Mathematica; 1999, 132, 1; 71-78
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new Kantorovich-type theorem for Newtons method
Autorzy:
Argyros, Ioannis
Powiązania:
https://bibliotekanauki.pl/articles/1338842.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Newton's method
Lipschitz-Hölder condition
Kantorovich hypothesis
Banach space
Opis:
A new Kantorovich-type convergence theorem for Newton's method is established for approximating a locally unique solution of an equation F(x)=0 defined on a Banach space. It is assumed that the operator F is twice Fréchet differentiable, and that F', F'' satisfy Lipschitz conditions. Our convergence condition differs from earlier ones and therefore it has theoretical and practical value.
Źródło:
Applicationes Mathematicae; 1999, 26, 2; 151-157
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximation of functions from \(L^p(\omega)_\beta\) by linear operators of their Fourier series
Autorzy:
Łenski, Włodzimierz
Szal, Bogdan
Powiązania:
https://bibliotekanauki.pl/articles/744850.pdf
Data publikacji:
2011
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Rate of approximation
Summability of Fourier series
Lipschitz classes
Opis:
We show the results corresponding to theorems of S. Lal [Appl. Math. Comput., 209 (2009) 346-350] on the rate of approximation of functions from the generalized integral Lipschitz classes by matrix summability means of their Fourier series as well as to the authors theorems [Acta Comment. Univ. Tartu. Math., 13 (2009), 11-24] also on such approximations.
Źródło:
Commentationes Mathematicae; 2011, 51, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Spaces of Lipschitz functions on metric spaces
Autorzy:
Pallaschke, Diethard
Pumplün, Dieter
Powiązania:
https://bibliotekanauki.pl/articles/729633.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
categories of Lipschitz spaces
Saks spaces
base normed spaces
Opis:
In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2015, 35, 1; 5-23
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Characterizations and classification of paraconvex multimaps
Autorzy:
Mokhtar-Kharroubi, Hocine
Powiązania:
https://bibliotekanauki.pl/articles/2183481.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
support function
paraconvex multimap
Lipschitz property
generalized convexities
submonotonicity
Opis:
Paraconvex multimaps are revisited in normed vector space setting. A parallel is provided with the studies conducted for real valued paraconvex functions on generalized convexities and monotonicities. Several characterizations are then obtained. The links with some generalized convexities for multimaps are examined and a first classification is achieved. In addition, two representation results for 2-paraconvex multimaps are given.
Źródło:
Control and Cybernetics; 2022, 51, 3; 303--325
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Order-Lipschitzian properties of multifunctions with applications to stability of efficient points
Autorzy:
Bednarczuk, E. M.
Powiązania:
https://bibliotekanauki.pl/articles/970514.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optymalizacja wektorowa
stabilność
vector optimization
stability
Lipschitz continuity of solutions
Opis:
We define order-Lipschitzian properties of multifunctions and we investigate local upper order-lipschitzness and order-calmness of efficient points of a set depending upon a parameter.
Źródło:
Control and Cybernetics; 2003, 32, 3; 491-502
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On [sigma]-porous and [Phi]-angle-small sets in metric spaces
Autorzy:
Rolewicz, S.
Powiązania:
https://bibliotekanauki.pl/articles/970531.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
zbiór porowaty
porous set
k-monotone family of Lipschitz functions
Opis:
It is shown that in metric spaces each [alpha, phi)-meagre set A is uniformly very porous and its index of uniform v-porosity is not smaller than [k-alpha/3k+alpha] provided that [phi] is a strictly k-monotone family of Lipschitz functions and [alpha] < k. The paper contains also conditions implying that a k-monotone family of Lipschitz functions is strictly k-monotone.
Źródło:
Control and Cybernetics; 2003, 32, 3; 671-681
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The boundary Harnack principle for the fractional Laplacian
Autorzy:
Bogdan, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/1220146.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
boundary Harnack principle
symmetric stable processes
harmonic functions
Lipschitz domains
Opis:
We study nonnegative functions which are harmonic on a Lipschitz domain with respect to symmetric stable processes. We prove that if two such functions vanish continuously outside the domain near a part of its boundary, then their ratio is bounded near this part of the boundary.
Źródło:
Studia Mathematica; 1997, 123, 1; 43-80
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Examples and counterexamples in Lipschitz analysis
Autorzy:
Fusek, P.
Klatte, D.
Kummer, B.
Powiązania:
https://bibliotekanauki.pl/articles/206846.pdf
Data publikacji:
2002
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
funkcja Lipschitza
nieprawidłowa funkcja Lipschitza
pochodna uogólniona
zastosowanie punktów stałych
application to stationary points
generalized derivatives
Lipschitz (multi-)functions
pathological Lipschitz functions
regularity concepts
Opis:
In the analysis of functions and multi-valued mappings of Lipschitzian type, there are many different notions of Lipschitz behavior, regularity and generalized derivatives. We collect relevant examples illustrating the interrelations between various concepts, the differences with the smooth case, and the importance of certain assumptions and special classes of Lipschitz mappings in applications.
Źródło:
Control and Cybernetics; 2002, 31, 3; 471-492
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities
Autorzy:
Papageorgiou, Nikolaos
Papalini, Francesca
Powiązania:
https://bibliotekanauki.pl/articles/1207915.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
eigenvalues
multivalued problem
discontinuous term
p-Laplacian
subdifferential
locally Lipschitz functional
Opis:
We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.
Źródło:
Annales Polonici Mathematici; 2000, 75, 2; 125-141
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On pointwise convergence of nets of Mellin-Kantorovich convolution operators
Autorzy:
Bardaro, Carlo
Mantellini, Ilaria
Powiązania:
https://bibliotekanauki.pl/articles/744939.pdf
Data publikacji:
2013
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Mellin-Kantorovich convolution operators, Mellin derivatives, moments, Lipschitz conditions, Voronovskaja formula
Opis:
Here we study pointwise approximation and asymptotic formulae for a class of Mellin-Kantorovich type integral operators, both in linear and nonlinear form.
Źródło:
Commentationes Mathematicae; 2013, 53, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces
Autorzy:
Gudovich, Anastasie
Kamenski, Mikhail
Nistri, Paolo
Powiązania:
https://bibliotekanauki.pl/articles/729318.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
singular perturbations
differential inclusions
analytic semigroups
multivalued compact operators
Lipschitz selections
Opis:
We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset $Z_L(ε)$ of the solution set of the singularly perturbed system. This subset is the set of the Hölder continuous solutions defined in [0,d], d > 0 with prescribed exponent and constant L. We show that $Z_L(ε)$ is uppersemicontinuous at ε = 0 in the C[0,d]×C[δ,d] topology for any δ ∈ (0,d].
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 2; 207-234
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximation by nonlinear integral operators in some modular function spaces
Autorzy:
Bardaro, Carlo
Musielak, Julian
Vinti, Gianluca
Powiązania:
https://bibliotekanauki.pl/articles/1311190.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
modular space
nonlinear integral operator
generalized Lipschitz condition
approximation by singular integrals
Opis:
Let G be a locally compact Hausdorff group with Haar measure, and let L⁰(G) be the space of extended real-valued measurable functions on G, finite a.e. Let ϱ and η be modulars on L⁰(G). The error of approximation ϱ(a(Tf - f)) of a function $f ∈ (L⁰(G))_{ϱ+η} ∩ Dom T$ is estimated, where $(Tf)(s) = ∫_G K(t-s,f(t))dt$ and K satisfies a generalized Lipschitz condition with respect to the second variable.
Źródło:
Annales Polonici Mathematici; 1996, 63, 2; 173-182
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On a result by Clunie and Sheil-Small
Autorzy:
Partyka, Dariusz
Sakan, Ken-ichi
Powiązania:
https://bibliotekanauki.pl/articles/747161.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Harmonic mappings
Lipschitz condition
bi-Lipchitz condition
co-Lipchitz condition
quasiconformal mappings
Opis:
In 1984 J. Clunie and T. Sheil-Small proved ([2, Corollary 5.8]) that for any complex-valued and sense-preserving injective harmonic mapping \(F\) in the unit disk \(\mathbb{D}\), if \(F(\mathbb{D})\) is a convex domain, then the inequality \(|G(z_2)-G(z_1)| < |H(z_2)- H(z_1)|\) holds for all distinct points \(z_1, z_2 \in \mathbb{D}\). Here \(H\) and \(G\) are holomorphic mappings in \(\mathbb{D}\) determined by \(F = H + \overline{G}\), up to a constant function. We extend this inequality by replacing the unit disk by an arbitrary nonempty domain \(\Omega\) in \(\mathbb{C}\) and improve it provided \(F\) is additionally a quasiconformal mapping in \(\Omega\).
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2012, 66, 2
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The shooting approach in analyzing bang-bang extremals with simultaneous control switches
Autorzy:
Felgenhauer, U.
Powiązania:
https://bibliotekanauki.pl/articles/969603.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
bang-bang control
Lipschitz stability in optimal control
nonsmooth optimization
shooting type methods
Opis:
The paper is devoted to stability investigation of optimal structure and switching points position for parametric bang-bang control problem with special focus on simultaneous switches of two control components. In contrast to problems where only simple switches occur, the switching points in general are no longer differentiable functions of input parameters. Conditions for Lipschitz stability are found which generalize known sufficient optimality conditions to nonsmooth situation. The analysis makes use of backward shooting representation of extremals, and of generalized implicit function theorems. The Lipschitz properties are illustrated for an example by constructing backward parameterized family of extremals and providing first-order switching points prediction.
Źródło:
Control and Cybernetics; 2008, 37, 2; 307-327
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The effect of rounding errors on a certain class of iterative methods
Autorzy:
Argyros, Ioannis
Powiązania:
https://bibliotekanauki.pl/articles/1208172.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Fréchet derivative
Lipschitz conditions
Newton-like method
inexact Newton-like method
Banach space
Opis:
In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newton-like methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitz-type hypotheses on the mth Fréchet derivative (m ≥ 2 an integer) instead of the first one, we provide sufficient convergence conditions for the inexact Newton-like method that is actually generated on the computer. Moreover, we show that the ratio of convergence improves under our conditions. Furthermore, we provide a wider choice of initial guesses than before. Finally, a numerical example is provided to show that our results compare favorably with earlier ones.
Źródło:
Applicationes Mathematicae; 2000, 27, 3; 369-375
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces
Autorzy:
Costarelli, Danilo
Vinti, Gianluca
Powiązania:
https://bibliotekanauki.pl/articles/745018.pdf
Data publikacji:
2013
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Nonlinear sampling Kantorovich operators, Orlicz spaces, order of approximation, Lipschitz classes, irregular sampling
Opis:
In this paper, we study the rate of approximation for the nonlinear sampling Kantorovich operators. We consider the case of uniformly continuous and bounded functions belonging to Lipschitz classes of the Zygmund-type, as well as the case of functions in Orlicz spaces. We estimate the aliasing errors with respect to the uniform norm and to the modular functional of the Orlicz spaces, respectively. The general setting of Orlicz spaces allows to deduce directly the results concerning the rate of convergence in \(L^p\)-spaces, \(1 \miu p\) < \(\infty\), very useful in the applications to Signal Processing. Others examples of Orlicz spaces as interpolation spaces and exponential spaces are discussed and the particular cases of the nonlinear sampling Kantorovich series constructed using Fej\'er and B-spline kernels are also considered.
Źródło:
Commentationes Mathematicae; 2013, 53, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Delay perturbed evolution problems involving time dependent subdifferential operators
Autorzy:
Saïdi, Soumia
Yarou, Mustapha
Powiązania:
https://bibliotekanauki.pl/articles/729544.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Differential inclusions
subdifferential operator
Lipschitz functions
set-valued map
delay
perturbation
absolutely continuous map
Opis:
We investigate in the present paper, the existence and uniqueness of solutions for functional differential inclusions involving a subdifferential operator in the infinite dimensional setting. The perturbation which contains the delay is single-valued, separately measurable, and separately Lipschitz. We prove, without any compactness condition, that the problem has one and only one solution.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 1; 61-87
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces.
Autorzy:
-Q. Bui, H.
Paluszyński, M.
Taibleson, M.
Powiązania:
https://bibliotekanauki.pl/articles/1287511.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Besov-Lipschitz space
Triebel-Lizorkin space
Littlewood-Paley function
Calderón representation theorem
$A_∞$ weight
Opis:
We give characterizations of weighted Besov-Lipschitz and Triebel-Lizorkin spaces with $A_∞$ weights via a smooth kernel which satisfies "minimal" moment and Tauberian conditions. The results are stated in terms of the mixed norm of a certain maximal function of a distribution in these weighted spaces.
Źródło:
Studia Mathematica; 1996, 119, 3; 219-246
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hemivariational inequalities governed by the p-Laplacian - Neumann problem
Autorzy:
Naniewicz, Z.
Powiązania:
https://bibliotekanauki.pl/articles/970247.pdf
Data publikacji:
2007
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
Neumann problem
noncoercive hemivariational inequality
unilateral growth condition
critical point theory
locally Lipschitz functional
Opis:
A hemivariational inequality involving p-Laplacian is studied under the hypothesis that the nonlinear part fulfills the unilateral growth condition. The existence of solutions for problems with Neumann boundary conditions is established by making use of Chang's version of the critical point theory for nonsmooth locally Lipschitz functionals, combined with the Galerkin method. The approach is based on the recession technique introduced previously by the author.
Źródło:
Control and Cybernetics; 2007, 36, 3; 727-754
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Convergence of finite-dimensional approximations for mixed-integer optimization with differential equations
Autorzy:
Hante, Falk M.
Schmidt, Martin
Powiązania:
https://bibliotekanauki.pl/articles/1839150.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimization
differential equations
optimal value function
Lipschitz continuity
parametric optimization
mixed integer nonlinear programming
Opis:
We consider a direct approach to solving the mixedinteger nonlinear optimization problems with constraints depending on initial and terminal conditions of an ordinary differential equation. In order to obtain a finite-dimensional problem, the dynamics are approximated using discretization methods. In the framework of general one-step methods, we provide sufficient conditions for the convergence of this approach in the sense of the corresponding optimal values. The results are obtained by considering the discretized problem as a parametric mixed-integer nonlinear optimization problem in finite dimensions, where the step size for discretization of the dynamics is the parameter. In this setting, we prove the continuity of the optimal value function under a stability assumption for the integer feasible set and second-order conditions from nonlinear optimization. We address the necessity of the conditions on the example of pipe sizing problems for gas networks.
Źródło:
Control and Cybernetics; 2019, 48, 2; 209-226
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adaptive observer-based fault estimation for a class of Lipschitz nonlinear systems
Autorzy:
Oucief, N.
Tadjine, M.
Labiod, S.
Powiązania:
https://bibliotekanauki.pl/articles/229517.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
nonlinear adaptive observer
fault estimation
strictly positive real
Lipschitz systems
observer matching condition
LMI
Opis:
Fault input channels represent a major challenge for observer design for fault estimation. Most works in this field assume that faults enter in such a way that the transfer functions between these faults and a number of measured outputs are strictly positive real (SPR), that is, the observer matching condition is satisfied. This paper presents a systematic approach to adaptive observer design for joint estimation of the state and faults when the SPR requirement is not verified. The proposed method deals with a class of Lipschitz nonlinear systems subjected to piecewise constant multiplicative faults. The novelty of the proposed approach is that it uses a rank condition similar to the observer matching condition to construct the adaptation law used to obtain fault estimates. The problem of finding the adaptive observer matrices is formulated as a Linear Matrix Inequality (LMI) optimization problem. The proposed scheme is tested on the nonlinear model of a single link flexible joint robot system.
Źródło:
Archives of Control Sciences; 2016, 26, 2; 245-259
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A sufficient condition for optimality in nondifferentiable invex programming
Autorzy:
Antczak, T.
Powiązania:
https://bibliotekanauki.pl/articles/205838.pdf
Data publikacji:
2001
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
funkcja półwypukła
uogólniony gradient Clarka
Clarke's generalized gradient
invex function
locally Lipschitz function
semiconvex function
Opis:
In this paper sufficient optimality condition are established for a nonlinear programming problem without differentiability assumption on the data wherein Clarke's generalized gradient is used to define invexity.
Źródło:
Control and Cybernetics; 2001, 30, 4; 431-437
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimality conditions and duality for generalized fractional minimax programming involving locally Lipschitz (b,Ψ,Φ,ρ) -univex functions
Autorzy:
Antczak, T.
Mishra, S. K.
Upadhyay, B. B.
Powiązania:
https://bibliotekanauki.pl/articles/206666.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
generalized fractional minimax programming
locally Lipschitz (b,Ψ,Φ,ρ)-univex function
optimality conditions
duality
Opis:
In this paper, we are concerned with optimality conditions and duality results of generalized fractional minimax programming problems. Sufficient optimality conditions are established for a class of nondifferentiable generalized fractional minimax programming problems, in which the involved functions are locally Lipschitz (b,Ψ,Φ,ρ)-univex. Subsequently, these optimality conditions are utilized as a basis for constructing various parametric and nonparametric duality models for this type of fractional programming problems and proving appropriate duality theorems.
Źródło:
Control and Cybernetics; 2018, 47, 1; 5-32
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Regularity and stability of optimal controls of nonstationary Navier-Stokes equations
Autorzy:
Wachsmuth, D.
Powiązania:
https://bibliotekanauki.pl/articles/970093.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie optymalne
równanie Naviera-Stokesa
stabilność Lipschitza
optimal control
Navier-Stokes equations
control constraints
Lipschitz stability
Opis:
The regularity and stability of optimal controls of nonstationary Navier-Stokes equations are investigated. Under suitable assumptions every control satisfying first-order necessary conditions is shown to be a continuous function in both space and time. Moreover, the behaviour of a locally optimal control under certain perturbations of the cost functional and the state equation is investigated. Lipschitz stability is proven provided a second-order sufficient optimality condition holds.
Źródło:
Control and Cybernetics; 2005, 34, 2; 387-409
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bernstein and van der Corput-Schaake type inequalities on semialgebraic curves
Autorzy:
Baran, M.
Pleśniak, W.
Powiązania:
https://bibliotekanauki.pl/articles/1219584.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Bernstein and van der Corput-Schaake type inequalities
semialgebraic curves
algebraic manifolds
pluricomplex Green function
Lipschitz functions
Opis:
We show that in the class of compact, piecewise $C^1$ curves K in $ℝ^n$, the semialgebraic curves are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for the derivatives of (the traces of) polynomials on K.
Źródło:
Studia Mathematica; 1997, 125, 1; 83-96
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
All solenoids of piecewise smooth maps are period doubling
Autorzy:
Alsedà, Lluís
Jiménez López, Víctor
Snoha, L’ubomír
Powiązania:
https://bibliotekanauki.pl/articles/1205307.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Markov graph
periodic point
piecewise smooth map with nowhere vanishing Lipschitz continuous derivative
piecewise linear map
solenoid
Opis:
We show that piecewise smooth maps with a finite number of pieces of monotonicity and nowhere vanishing Lipschitz continuous derivative can have only period doubling solenoids. The proof is based on the fact that if $p_1 < ... < p_n$ is a periodic orbit of a continuous map f then there is a union set ${q_1,..., q_{n-1}}$ of some periodic orbits of f such that $p_i < q_i < p_{i+1}$ for any i.
Źródło:
Fundamenta Mathematicae; 1998, 157, 2-3; 121-138
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Representations of hypersurfaces and minimal smoothness of the midsurface in the theory of shells
Autorzy:
Delfour, M. C.
Powiązania:
https://bibliotekanauki.pl/articles/970297.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
thin shell
asymptotic shell
midsurface
smoothness
representation of a surface
oriented distance function
bi-Lipschitz mapping
tubular neighborhood
Opis:
Many hypersurfaces ω in R^N can be viewed as a subset of the boundary Γ of an open subset Ω of R^N. In such cases, the gradient and Hessian matrix of the associated oriented distance function ba to the underlying set Ω completely describe the normal and the N fundamental forms of ω, and a fairly complete intrinsic theory of Sobolev spaces on C1'1-hypersurfaces is available in Delfour (2000). In the theory of thin shells, the asymptotic model only depends on the choice of the constitutive law, the midsurface, and the space of solutions that properly handles the loading applied to the shell and the boundary conditions. A central issue is the minimal smoothness of the midsurface to still make sense of asymptotic membrane shell and bending equations without ad hoc mechanical or mathematical assumptions. This is possible for a C1'1-midsurface with or without boundary and without local maps, local bases, and Christoffel symbols via the purely intrinsic methods developed by Delfour and Zolesio (1995a) in 1992. Anicic, LeDret and Raoult (2004) introduced in 2004 a family of surfaces ω that are the image of a connected bounded open Lipschitzian domain in R² by a bi-Lipschitzian mapping with the assumption that the normal field is globally Lipschizian. >From this, they construct a tubular neighborhood of thickness 2h around the surface and show that for sufficiently small h the associated tubular neighborhood mapping is bi-Lipschitzian. We prove that such surfaces are C1'1-surfaces with a bounded measurable second fundamental form. We show that the tubular neighborhood can be completely described by the algebraic distance function to ω and that it is generally not a Lipschitzian domain in R³ by providing the example of a plate around a flat surface ω verifying all their assumptions. Therefore, the G1-join of K-regular patches in the sense of Le Dret (2004) generates a new K-regular patch that is a C1'1-surface and the join is C1'1. Finally, we generalize everything to hypersurfaces generated by a bi-Lipschitzian mapping defined on a domain with facets (e.g. for sphere, torus). We also give conditions for the decomposition of a C1'1-hypersurface into C1'1-patches.
Źródło:
Control and Cybernetics; 2008, 37, 4; 879-911
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On robustness of the regularity property of maps
Autorzy:
Ioffe, A. D.
Powiązania:
https://bibliotekanauki.pl/articles/970517.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
prawidłowość metryczna
nachylenie
kryterium prawidłowości
metric regularity
openness at a linear rate
pseudo-Lipschitz (Aubin) property
regularity criterion
Opis:
The problem considered in the paper can be described as follows. We are given a continuous mapping from one metric space into another which is regular (in the sense of metric regularity or, equivalently, controllability at a linear rate) near a certain point. How small may be an additive perturbation of the mapping which destroys regularity? The paper contains a new proof of a recent theorem of Dontchev-Lewis-Rockafellar for linear perturbations of maps between finite-dimensional Banach spaces and an exact estimate for Lipschitz perturbations of maps between complete metric spaces.
Źródło:
Control and Cybernetics; 2003, 32, 3; 543-554
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Lipschitz stability of optimal controls for the steady-state Navier-Stokes equations
Autorzy:
Roubicek, T.
Troltzsch, F.
Powiązania:
https://bibliotekanauki.pl/articles/970527.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie strumieniem danych
stabilność Lipschitza
incompressible viscous fluids
flow control
first and second order optimality conditions
Lipschitz stability
Opis:
An optimal control problem with quadratic cost functional for the steady-state Navier-Stokes equations with no-slip boundary condition is considered. Lipschitz stability of locally optimal controls with respect to certain perturbations of both the cost functional and the equation is proved provided a second-order sufficient optimality condition holds. For a sufficiently small Reynolds number, even global Lipschitz stability of the unique optimal control is shown.
Źródło:
Control and Cybernetics; 2003, 32, 3; 683-705
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Practical Mittag-Leffler stability of quasi-one-sided Lipschitz fractional order systems
Autorzy:
Basdouri, Imed
Kasmi, Souad
Lerbet, Jean
Powiązania:
https://bibliotekanauki.pl/articles/27312007.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
fractional-order systems
Caputo derivative
quasi-one-sided Lipschitz condition
nonlinear systems
observer design
output feedback stabilization
separation principle
Opis:
This paper focuses on the global practical Mittag-Leffler feedback stabilization problem for a class of uncertain fractional-order systems. This class of systems is a larger class of nonlinearities than the Lipschitz ones. Based on the quasi-one-sided Lipschitz condition, firstly, we provide sufficient conditions for the practical observer design. Then, we exhibit that practical Mittag-Leffler stability of the closed loop system with a linear, state feedback is attained. Finally, a separation principle is established and we prove that the closed loop system is practical Mittag-Leffler stable.
Źródło:
Archives of Control Sciences; 2023, 33, 1; 55--70
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Discontinuous quasilinear elliptic problems at resonance
Autorzy:
Kourogenis, Nikolaos
Papageorgiou, Nikolaos
Powiązania:
https://bibliotekanauki.pl/articles/966108.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
compact embedding
Poincaré's inequality
Palais-Smale condition
critical point
variational method
Mountain Pass Theorem
subdifferential
problems at resonance
locally Lipschitz functional
Opis:
In this paper we study a quasilinear resonant problem with discontinuous right hand side. To develop an existence theory we pass to a multivalued version of the problem, by filling in the gaps at the discontinuity points. We prove the existence of a nontrivial solution using a variational approach based on the critical point theory of nonsmooth locally Lipschitz functionals.
Źródło:
Colloquium Mathematicum; 1998, 78, 2; 213-223
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Lipschitz stability of solutions to parametric optimal control for elliptic equations
Autorzy:
Malanowski, K.
Troeltzsch, F.
Powiązania:
https://bibliotekanauki.pl/articles/205516.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
równanie eliptyczne
stabilność
sterowanie optymalne
elliptic equation
generalized equations
Lipschitz stability of the solutions
non-linear boundary control
parametric optimal control
Opis:
: A family of parameter dependent elliptic optimal control problems with nonlinear boundary control is considered. The control function is subject to amplitude constraints. A characterization of conditions is given under which solutions to the problems exist, are locally unique and Lipschitz continuous in a neighborhood of the reference value of the parameter.
Źródło:
Control and Cybernetics; 2000, 29, 1; 237-256
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hemivariational inequalities governed by the p-Laplacian -Dirichlet problem
Autorzy:
Naniewicz, Z.
Powiązania:
https://bibliotekanauki.pl/articles/970356.pdf
Data publikacji:
2004
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
zagadnienie Dirichleta
nierówność hemiwariacyjna
jednostronny warunek wzrostu
teoria punktu krytycznego
Dirichlet problem
hemivariational inequality
unilateral growth condition
critical point theory
locally Lipschitz functional
Opis:
A hemivariational inequality involving p-Laplacian is studied under the hypothesis that the nonlinear part fulfills the unilateral growth condition (Naniewicz, 1994). The existence of solutions for problems with Dirichlet boundary conditions is established by making use of Chang's version of the critical point theory for non-smooth locally Lipschitz functionals (Chang, 1981), combined with the Galerkin method. A class of problems with nonlinear potentials fulfilling the classical growth hypothesis without Ainbrosetti-Rabinowitz type assumption is discussed. The approach is based on the recession technique introduced in Naniewicz (2003).
Źródło:
Control and Cybernetics; 2004, 33, 2; 181-210
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Automatic simplification of the geometry of a cartographic line using contractive self-mapping – illustrated with an example of a polyline band
Autorzy:
Bac-Bronowicz, Joanna
Banasik, Piotr
Chrobak, Tadeusz
Powiązania:
https://bibliotekanauki.pl/articles/29433667.pdf
Data publikacji:
2023-12-07
Wydawca:
Oddział Kartograficzny Polskiego Towarzystwa Geograficznego
Tematy:
digital generalization
contractive self-mapping
Salichtchev’s minimum measures
geometry of a polyline in the binary tree structure
Lipschitz’s contraction triangle
Banach theorem
Opis:
The present article is another attempt to adapt map geometry to automatic digital cartography. The paper presents a method of digital polyline generalisation that uses contractive self-mapping. It is a method of simplification, not just an algorithm for simplification. This method in its 1996 version obtained a patent entitled “Method of Eliminating Points in the Process of Numerical Cartographic Generalisation” – Patent Office of the Republic of Poland, No. 181014, 1996. The first results of research conducted using the presented method, with clearly defined data (without singular points of their geometry), were published in the works of the authors in 2021 and 2022. This article presents a transition from the DLM (Digital Landscape Model) to the DCM (Digital Cartographic Model). It demonstrates an algorithm with independent solutions for the band axis and both its edges. The presented example was performed for the so-called polyline band, which can represent real topographic linear objects such as rivers and boundaries of closed areas (buildings, lakes, etc.). An unambiguous representation of both edges of the band is its axis, represented in DLM, which can be simplified to any scale. A direct consequence of this simplification is the shape of the band representing the actual shape of both edges of the object that is classified in the database as a linear object in DCM. The article presents an example performed for the so-called polyline band, which represents real topographic linear objects (roads, rivers) and area boundaries. The proposed method fulfils the following conditions: the Lipschitz condition, the Cauchy condition, the Banach theorem, and the Salichtchev’s standard for object recognition on the map. The presented method is objective in contrast to the previously used approximate methods, such as generalisations that use graph theory and fractal geometry, line smoothing and simplification algorithms, statistical methods with classification of object attributes, artificial intelligence, etc. The presented method for changing the geometry of objects by any scale of the map is 100% automatic, repeatable, and objective; that is, it does not require a cartographer’s intervention.
Źródło:
Polish Cartographical Review; 2023, 55, 1; 73-86
2450-6974
Pojawia się w:
Polish Cartographical Review
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Schramm spaces and composition operators
Autorzy:
Wróbel, Małgorzata
Powiązania:
https://bibliotekanauki.pl/articles/24201507.pdf
Data publikacji:
2023
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Schramm function
continuous function
Nemytskij composition operator
Schramm type variation
uniformly continuous operator
Lipschitz operator
funkcja Schramma
funkcja ciągła
operator kompozycji Niemyckiego
operator jednostajnie ciągły
operator Lipschitza
Opis:
We give some properties of Schramm functions; among others, we prove that the family of all continuous piecewise linear functions defined on a real interval I is contained in the space ΦBV (I) of functions of bounded variation in the sense of Schramm. Moreover, we show that the generating function of the corresponding Nemytskij composition operator acting between Banach spaces CΦBV (I) of continuous functions of bounded Schramm variation has to be continuous and additionally we show that a space CΦBV (I) has the Matkowski property.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 2; 87--98
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of semilinear elliptic equation with state constraint : maximum principle for minimizing sequence, regularity, normality, sensitivity
Autorzy:
Sumin, M.
Powiązania:
https://bibliotekanauki.pl/articles/205729.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
równanie eliptyczne
sensitivity
sterowanie optymalne
zasada maksimum
elliptic equation
Lipschitz continuity
maximum principle
minimizing sequence
normality
optimal control
parametric optimal control
pointwise state constraint
regularity
sequences
value function
Opis:
This article deals with state constrained optimal control problem for semilinear elliptic equation in a domain Omega. The state constraint is lumped on the compactum X contained in/implied by Omega n and contains a functional parameter q in C(X ). It is shown that any minimizing approximate solution (m.a.s.) in the sense of J. Warga satisfies the pointwise maximum principle (the maximum principle for m.a.s.) if the problem is meaningful, i.e., the value of the problem is finite. It is also shown that a condition of Slater's type is sufficient for the normality in the so-called "linear-convex" problem, and the normality of the problem for some fixed value of the parameter q in C(X ) implies the Lipschitz continuity of its value function in a neighborhood of q. The paper contains illustrative examples.
Źródło:
Control and Cybernetics; 2000, 29, 2; 449-472
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-50 z 53

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