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Wyświetlanie 1-15 z 469
Tytuł:
Fuzzy mappings
Autorzy:
Heilpern, Stanisław
Powiązania:
https://bibliotekanauki.pl/articles/747379.pdf
Data publikacji:
1983
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Fuzzy topology
Fuzzy set theory
Fixed-point and coincidence theorems
Opis:
.
Let X be the class of all fuzzy subsets of a metric space X. A fuzzy subset A is called an approximate value if A is a closed and convex fuzzy subset with supA(x)=1; the class of all such elements is denoted by W(X), and it is a metric space with the distance D(A,B)=sup dist(Aα,Bα), where Aα and Bα denote the α-level of A and B, respectively, and dist( , ) denotes the generalized Hausdorff distance [see, e.g., M. P. Chen and M. H. Shin , J. Math. Anal. Appl. 71 (1979), no. 2, 516–524; MR0548780]. The author is especially concerned with W(R). Algebraic operations in W(R) are defined and basic rules for arithmetic operations on approximate values are proved. Moreover, functions with values in W(R) are also investigated. Finally, a fixed point theorem for fuzzy mappings is stated and an example is given [for the proof see the author, ibid. 83 (1981), no. 2, 566–569; MR0641351].
Źródło:
Mathematica Applicanda; 1983, 11, 22
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new convexity property that implies a fixed point property for $L_{1}$
Autorzy:
Lennard, Chris
Powiązania:
https://bibliotekanauki.pl/articles/1293465.pdf
Data publikacji:
1991
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
uniform Kadec-Klee property
convergence in measure compact sets
convex sets
normal structure
Lebesgue function spaces
fixed point
nonexpansive mapping
Chebyshev centre
Opis:
In this paper we prove a new convexity property for L₁ that resembles uniform convexity. We then develop a general theory that leads from the convexity property through normal structure to a fixed point property, via a theorem of Kirk. Applying this theory to L₁, we get the following type of normal structure: any convex subset of L₁ of positive diameter that is compact for the topology of convergence locally in measure, must have a radius that is smaller than its diameter. Indeed, a stronger result holds. The Chebyshev centre of any norm bounded, convergence locally in measure compact subset of L₁ must be norm compact. Immediately from normal structure, we get a new proof of a fixed point theorem for L₁ due to Lami Dozo and Turpin.
Źródło:
Studia Mathematica; 1991, 100, 2; 95-108
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Contractive projections on the fixed point set of $L_∞$ contractions
Autorzy:
Lin, Michael
Sine, Robert
Powiązania:
https://bibliotekanauki.pl/articles/1396184.pdf
Data publikacji:
1991
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
$L_∞$
projection
contraction
binary ball intersection
ergodic
positive operator
fixed point
Źródło:
Colloquium Mathematicum; 1991, 62, 1; 91-96
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nielsen theory of transversal fixed point sets (with an appendix: $C^∞$ and $C^0$ fixed point sets are the same, by R. E. Greene)
Autorzy:
Schirmer, Helga
Powiązania:
https://bibliotekanauki.pl/articles/1214996.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
transversally fixed maps
minimal and arbitrary fixed point sets
Nielsen fixed point theory
relative and extension Nielsen numbers
Opis:
Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of fixed points in cases where continuous map extensions behave differently from smooth ones. In the appendix it is shown that a subset of a smooth manifold can be realized as the fixed point set of a smooth map in a given homotopy class if and only if it can be realized as the fixed point set of a continuous one. A special case of this result is used in a proof of the paper.
Źródło:
Fundamenta Mathematicae; 1992, 141, 1; 31-59
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem
Autorzy:
Wong, Peter
Powiązania:
https://bibliotekanauki.pl/articles/1215078.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
fixed points
coincidences
roots
Lefschetz number
Nielsen number
Opis:
Let $f,g:M_1 → M_2$ be maps where $M_1$ and $M_2$ are connected triangulable oriented n-manifolds so that the set of coincidences $C_{f,g}= {x ∈ M_1 | f(x)=g(x)}$ is compact in $M_1$. We define a Nielsen equivalence relation on $C_{f,g}$ and assign the coincidence index to each Nielsen coincidence class. In this note, we show that, for n ≥ 3, if $M_2= \widetilde M_2/K$ where $\widetilde M_2$ is a connected simply connected topological group and K is a discrete subgroup then all the Nielsen coincidence classes of f and g have the same coincidence index. In particular, when $M_1$ and $M_2$ are compact, f and g are deformable to be coincidence free if the Lefschetz coincidence number L(f,g) vanishes.
Źródło:
Fundamenta Mathematicae; 1991-1992, 140, 2; 191-196
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on the converse of the Lefschetz theorem for G-maps
Autorzy:
Izydorek, M.
Vidal, A.
Powiązania:
https://bibliotekanauki.pl/articles/1311838.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
equivariant Nielsen number
G-simplicial complex
equivariant map
fixed point
Opis:
The purpose of this note is to prove the converse of the Lefschetz fixed point theorem (CLT) together with an equivariant version of the converse of the Lefschetz deformation theorem (CDT) in the category of finite G-simplicial complexes, where G is a finite group.
Źródło:
Annales Polonici Mathematici; 1993, 58, 2; 177-183
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The automorphism groups of Zariski open affine subsets of the affine plane
Autorzy:
Jelonek, Zbigniew
Powiązania:
https://bibliotekanauki.pl/articles/1311651.pdf
Data publikacji:
1994
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
polynomial automorphisms
the set of fixed points of a polynomial automorphism
the affine plane
Opis:
We study some properties of the affine plane. First we describe the set of fixed points of a polynomial automorphism of ℂ². Next we classify completely so-called identity sets for polynomial automorphisms of ℂ². Finally, we show that a sufficiently general Zariski open affine subset of the affine plane has a finite group of automorphisms.
Źródło:
Annales Polonici Mathematici; 1994-1995, 60, 2; 163-171
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Borel partitions of unity and lower Carathéodory multifunctions
Autorzy:
Srivastava, S.
Powiązania:
https://bibliotekanauki.pl/articles/1208394.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Carathéodory functions and multifunctions
Carathéodory selections
fixed points
Opis:
We prove the existence of Carathéodory selections and representations of a closed convex valued, lower Carathéodory multifunction from a set A in $A(ℰ ⊗ ℬ(X))$ into a separable Banach space Y, where ℰ is a sub-σ-field of the Borel σ-field ℬ(E) of a Polish space E, X is a Polish space and A is the Suslin operation. As applications we obtain random versions of results on extensions of continuous functions and fixed points of multifunctions. Such results are useful in the study of random differential equations and inclusions and in mathematical economics.
  As a key tool we prove that if A is an analytic subset of E × X and if ${U_n : n ∈ w}$ is a sequence of Borel sets in A such that $A=∪_n U_n$ and the section $U_n(e)$ is open in A(e), e ∈ E, n ∈ w, then there exist Borel functions $p_n : A → [0,1]$, n ∈ w, such that for every e ∈ E, ${p_n(e,·) : n ∈ w}$ is a locally Lipschitz partition of unity subordinate to ${U_n(e) : n ∈ w}$.
Źródło:
Fundamenta Mathematicae; 1994-1995, 146, 3; 239-249
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On positive solutions of a class of second order nonlinear differential equations on the halfline
Autorzy:
Staněk, Svatoslav
Powiązania:
https://bibliotekanauki.pl/articles/1311424.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
nonlinear second order differential equation
nonnegative solution
existence and uniqueness of solutions
bounded solution
dependence of solutions on the parameter
boundary value problem on a noncompact interval
Tikhonov-Schauder fixed point theorem
Opis:
The differential equation of the form $(q(t)k(u)(u')^a)' = f(t)h(u)u'$, a ∈ (0,∞), is considered and solutions u with u(0) = 0 and (u(t))² + (u'(t))² > 0 on (0,∞) are studied. Theorems about existence, uniqueness, boundedness and dependence of solutions on a parameter are given.
Źródło:
Annales Polonici Mathematici; 1995, 62, 2; 123-142
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weak uniform normal structure and iterative fixed points of nonexpansive mappings
Autorzy:
Domínguez Benavides, T.
López Acedo, G.
Xu, Hong
Powiązania:
https://bibliotekanauki.pl/articles/967052.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
nonexpansive mapping
iterative fixed point
geometrical coefficients of Banach spaces
James' quasi-reflexive space
weak uniform normal structure
Opis:
This paper is concerned with weak uniform normal structure and iterative fixed points of nonexpansive mappings. Precisely, in Section 1, we show that the geometrical coefficient β(X) for a Banach space X recently introduced by Jimenez-Melado [8] is exactly the weakly convergent sequence coefficient WCS(X) introduced by Bynum [1] in 1980. We then show in Section 2 that all kinds of James' quasi-reflexive spaces have weak uniform normal structure. Finally, in Section 3, we show that in a space X with weak uniform normal structure, every nonexpansive self-mapping defined on a weakly sequentially compact convex subset of X admits an iterative fixed point.
Źródło:
Colloquium Mathematicum; 1995, 68, 1; 17-23
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Note on weakly inward mappings
Autorzy:
Fečkan, Michal
Powiązania:
https://bibliotekanauki.pl/articles/1311239.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
weakly inward maps
Nielsen fixed point theory
retractability
Opis:
The Nielsen fixed point theory is used to show several results for certain operator equations involving weakly inward mappings.
Źródło:
Annales Polonici Mathematici; 1996, 63, 1; 1-5
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Schauder fixed point theorem
Autorzy:
Górniewicz, Lech
Rozpłoch-Nowakowska, Danuta
Powiązania:
https://bibliotekanauki.pl/articles/1358988.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
absolute retract
set-valued operators
degree
fixed point
Opis:
The paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.
Źródło:
Banach Center Publications; 1996, 35, 1; 207-219
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Partially dissipative periodic processes
Autorzy:
Andres, Jan
Górniewicz, Lech
Lewicka, Marta
Powiązania:
https://bibliotekanauki.pl/articles/1358930.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
large-period forced oscillations
partial dissipativity
Poincaré translation operator
fixed point index
differential inclusions
Periodic processes
Opis:
Further extension of the Levinson transformation theory is performed for partially dissipative periodic processes via the fixed point index. Thus, for example, the periodic problem for differential inclusions can be treated by means of the multivalued Poincaré translation operator. In a certain case, the well-known Ważewski principle can also be generalized in this way, because no transversality is required on the boundary.
Źródło:
Banach Center Publications; 1996, 35, 1; 109-118
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An attraction result and an index theorem for continuous flows on $ℝ^n × [0,∞)$
Autorzy:
Wójcik, Klaudiusz
Powiązania:
https://bibliotekanauki.pl/articles/1310584.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Conley index
fixed point index
permanence
Opis:
We study the behavior of a continuous flow near a boundary. We prove that if φ is a flow on $E = ℝ^{n+1}$ for which $∂E = ℝ^n × {0}$ is an invariant set and S ⊂ ∂E is an isolated invariant set, with non-zero homological Conley index, then there exists an x in E\∂E such that either α(x) or ω(x) is in S. We also prove an index theorem for a flow on $ℝ^n × [0,∞)$.
Źródło:
Annales Polonici Mathematici; 1996-1997, 65, 3; 203-211
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fixed points of Lipschitzian semigroups in Banach spaces
Autorzy:
Górnicki, Jarosław
Powiązania:
https://bibliotekanauki.pl/articles/1218872.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Lipschitzian semigroup
fixed point
p-uniformly convex Banach space
Opis:
We prove the following theorem: Let p > 1 and let E be a real p-uniformly convex Banach space, and C a nonempty bounded closed convex subset of E. If $T = {T_s: C → C: s ∈ G = [0,∞)}$ is a Lipschitzian semigroup such that $g = lim inf_{G ∋ α → ∞} inf_{G ∋ δ ≥ 0} 1/α ʃ^α_0 ∥T_{β+δ}∥^p dβ < 1 + c$, where c > 0 is some constant, then there exists x ∈ C such that $T_sx = x$ for all s ∈ G.
Źródło:
Studia Mathematica; 1997, 126, 2; 101-113
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 469

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