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Tytuł:
FG-coupled fixed point theorems for contractive type mappings in partially ordered metric spaces
Autorzy:
Karichery, D.
Pulickakunnel, S.
Powiązania:
https://bibliotekanauki.pl/articles/357853.pdf
Data publikacji:
2018
Wydawca:
Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:
FG-coupled fixed point
mixed monotone property
contractive type mappings
partially ordered space
punkt stały
właściwość monotoniczna
przestrzeń częściowo uporządkowana
Opis:
In this paper we prove FG-coupled fixed point theorems for Kannan, Reich and Chatterjea type mappings in partially ordered complete metric spaces using mixed monotone property.
Źródło:
Journal of Mathematics and Applications; 2018, 41; 157-170
1733-6775
2300-9926
Pojawia się w:
Journal of Mathematics and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On \(\ell_1\)-preduals distant by 1
Autorzy:
Piasecki, Łukasz
Powiązania:
https://bibliotekanauki.pl/articles/747045.pdf
Data publikacji:
2018
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Banach-Mazur distance
nearly (almost) isometric Banach spaces
\(\ell_1\)-preduals, hyperplanes in c, weak\(^*\) fixed point property
stable weak\(^*\) fixed point property
almost stable weak\(^*\) fixed point property
nonexpansive mappings
Opis:
For every predual \(X\) of \(\ell_1\) such that the standard basis in \(\ell_1\) is weak\(^*\) convergent, we give explicit models of all Banach spaces \(Y\) for which the Banach-Mazur distance \(d(X,Y)=1\). As a by-product of our considerations, we obtain some new results in metric fixed point theory. First, we show that the space \(\ell_1\), with a predual \(X\) as above, has the stable weak\(^*\) fixed point property if and only if it has almost stable weak\(^*\) fixed point property, i.e. the dual \(Y^*\) of every Banach space \(Y\) has the weak\(^*\) fixed point property (briefly, \(\sigma(Y^*,Y)\)-FPP) whenever \(d(X,Y)=1\). Then, we construct a predual \(X\) of \(\ell_1\) for which \(\ell_1\) lacks the stable \(\sigma(\ell_1,X)\)-FPP but it has almost stable \(\sigma(\ell_1,X)\)-FPP, which in turn is a strictly stronger property than the \(\sigma(\ell_1,X)\)-FPP. Finally, in the general setting of preduals of \(\ell_1\), we give a sufficient condition for almost stable weak\(^*\) fixed point property in \(\ell_1\) and we prove that for a wide class of spaces this condition is also necessary.
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:
The generalized Day norm. Part II. Applications
Autorzy:
Budzyńska, Monika
Grzesik, Aleksandra
Kot, Mariola
Powiązania:
https://bibliotekanauki.pl/articles/747182.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Diametrically complete set
Day norm, fixed point
Kadec-Klee property
LUR space
nonexpansive mapping
non-strict Opial property
1-unconditional Schauder bases
Opis:
In this paper we prove that for each \(1< p, \tilde{p} < \infty\), the Banach space \((l^{\tilde{p}}, \left\|\cdot\right\|_{\tilde{p}})\) can be equivalently renormed in such a way that  the Banach space \((l^{\tilde{p}},\left\|\cdot\right\|_{L,\alpha,\beta,p,\tilde{p}})\) is LUR and has a diametrically complete set with empty interior. This result extends the Maluta theorem about existence of such a set in \(l^2\) with the Day norm. We also show that the Banach space \((l^{\tilde{p}},\left\|\cdot\right\|_{L,\alpha,\beta,p,\tilde{p}})\) has the weak fixed point property for nonexpansive mappings.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2017, 71, 2
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
WORTH property, García-Falset coefficient and Opial property of infinite sums
Autorzy:
Hardtke, Jan-David
Powiązania:
https://bibliotekanauki.pl/articles/746830.pdf
Data publikacji:
2015
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Opial property
uniform Opial property
WORTH property
Garc\'{i}a-Falset coefficient
absolute sums
fixed point property
Lebesgue-Bochner spaces
Opis:
We prove some results concerning the WORTH pro\-perty and the Garc\'{i}a-Falset coefficient of absolute sums of infinitely many Banach spaces. Also, the Opial property/uniform Opial property of infinite \(\ell^p\)-sums is studied, and some properties analogous to the Opial property/uniform Opial property are discussed for Lebesgue\polishendash Bochner spaces \(L^p(\mu,X)\).
Źródło:
Commentationes Mathematicae; 2015, 55, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotically isometric and isometric copies of \(\ell_1\) in some Banach function lattices
Autorzy:
Kamińska, Anna
~Mastyło, Mieczysław
Powiązania:
https://bibliotekanauki.pl/articles/1912874.pdf
Data publikacji:
2013
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Caldern-Lozanovskii spaces
Orlicz-Lorentz spaces
Orlicz spaces
Lorentz spaces
Marcinkiewicz spaces
isometric copies of \(\ell_1^{(n)}\) and \(\ell_1\)
asymptotically isometric copies of \(\ell_1\)
fixed point property
Opis:
We identify the class of Caldern-Lozanovskii spaces that do not contain an asymptotically isometric copy of \(\ell_1\), and consequently we obtain the corresponding characterizations in the classes of Orlicz-Lorentz and Orlicz spaces equipped with the Luxemburg norm. We also give a~complete description of order continuous Orlicz-Lorentz spaces which contain (order) isometric copies of \(\ell_1^{(n)}\) for each integer \(n \geq 2\).~As an application we provide necessary and sufficient conditions for order continuous Orlicz-Lorentz spaces to contain an (order) isometric copy of \(\ell_1\).~In particular we give criteria in Orlicz and Lorentz spaces for (order) isometric containment of \(\ell_1^{(n)}\) and \(\ell_1\).~The results are applied to obtain the~description of universal Orlicz-Lorentz spaces for all two-dimensional normed spaces.
Źródło:
Commentationes Mathematicae; 2013, 53, 2; 383-400
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weak nearly uniform smoothness of the \(\psi\)-direct sums \((X_1 \oplus \dots\oplus X_N)_\psi\)
Autorzy:
Kato, Mikio
Tamura, Takayuki
Powiązania:
https://bibliotekanauki.pl/articles/746388.pdf
Data publikacji:
2012
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
absolute norm
convex function
\(\psi\)-direct sum of Banach spaces
weak nearly uniform smoothness
Garcı́a-Falset coefficient
Schur property
fixed point property
Opis:
We shall characterize the weak nearly uniform smoothness of the \(\psi\)-direct sum \((X_1\oplus \dots\oplus X_N)_\psi\) of \(N\) Banach spaces \(X_1,\dots,X_N\), where \(\psi\) is a convex function satisfying certain conditions on the convex set \(\Delta_N = \{(s_1 ,\dots , s_{N-1})\in \mathbb{R}_+^{N-1} : \sum_{i=1}^{N-1} s_i \leq 1\). To do this a class of convex functions which yield \(\ell_1\)-like norms will be introduced. We shall apply our result to the fixed point property for nonexpansive mappings (FPP). In particular an example will be presented which indicates that there are plenty of Banach spaces with FPP failing to be uniformly non-square.
Źródło:
Commentationes Mathematicae; 2012, 52, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Uniform non-\(\ell^n_1\)-ness of \(\ell_\infty\)-sums of Banach spaces
Autorzy:
Kato, Mikio
Tamura, Takayuki
Powiązania:
https://bibliotekanauki.pl/articles/746532.pdf
Data publikacji:
2009
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
\(\ell_\infty\)-sum of Banach spaces
uniformly non-square space
uniformly non-\(\ell^n_1\)-space, super-reflexivity
fixed point property
constant \(R(a, X)\).
Opis:
We shall characterize the uniform non-\(\ell^n_1\)-ness of \(\ell_\infty\)-sums of Banach spaces \((X_1 \oplus \dots\oplus X_m)_\infty\). As applications, some results on super-reflexivity and the fixed point property for nonexpansive mappings will be presented.
Źródło:
Commentationes Mathematicae; 2009, 49, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of solutions of some quadratic integral equations
Autorzy:
Anichini, G.
Conti, G.
Powiązania:
https://bibliotekanauki.pl/articles/255299.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fixed-point property
measure of noncompactness
compact mappings
acyclic valued
quadratic integral equation
Opis:
In this paper we study the existence of continuous solutions of quadratic integral equations. The theory of quadratic integral equations has many useful applications in mathematical physics, economics, biology, as well as in describing real world problems. The main tool used in our investigations is a fixed point result for the multivalued solution's map with acyclic values.
Źródło:
Opuscula Mathematica; 2008, 28, 4; 433-440
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Uniform non-\(\ell_1^n\)-ness of \(\ell_1\)-sums of Banach spaces
Autorzy:
Kato, Mikio
Tamura, Takayuki
Powiązania:
https://bibliotekanauki.pl/articles/1912852.pdf
Data publikacji:
2007
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
\(\ell_1\)-sum of Banach spaces
uniformly non-square space
uniformly non-\(\ell_1^n\)-space
super-reflexivity
fixed point property
Opis:
We shall characterize the uniform non-\(\ell_1^n\)-ness of the \(\ell_1\)-sum \((X_1 \oplus\dots\oplus X_m)_1\) of a finite number of Banach spaces \(X_1 ,\dots, X_m\). Also we shall obtain that \((X_1 \oplus \dots \oplus X_m)_1\) is uniformly non-\(\ell_1^{m+1}\) if and only if all \(X_1 ,\dots , X_m\) are uniformly non-square (note that \((X_1 \oplus \dots \oplus X_m)_1\) is not uniformly non-\(\ell_1^m\)). Several related results will be presented.
Źródło:
Commentationes Mathematicae; 2007, 47, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weak nearly uniform soothness and worth property of \(\psi\)-direct sums of Banach spaces
Autorzy:
Kato, Mikio
Tamura, Takayuki
Powiązania:
https://bibliotekanauki.pl/articles/746218.pdf
Data publikacji:
2006
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
absolute norm
convex function
\(\psi\)-direct sum of Banach spaces
weak nearly uniform smoothness
Garcia-Falset coefficient
Schur property
WORTH property
uniform non-squareness
fixed point property
Opis:
We shall characterize the weak nearly uniform smoothness of the \(\psi\)-direct sum \(X \oplus_\psi Y\) of Banach spaces \(X\) and \(Y\). The Schur and WORTH properties will be also characterized. As a consequence we shall see in the \(\ell_\infty\)-sums of Banach spaces there are many examples of Banach spaces with the fixed point property which are not uniformly non-square.
Źródło:
Commentationes Mathematicae; 2006, 46, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
New versions on Nikaidôs coincidence theorem
Autorzy:
Chu, Liang-Ju
Lin, Ching-Yan
Powiązania:
https://bibliotekanauki.pl/articles/729530.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Vietoris map
Nikaidô's coincidence theorem
Fan-type element
Górniewicz-type fixed point theorem
coincidence
variational inequality
acyclic multifunction
partition of unity
local intersection property
KKM mapping
locally selectionable multifunction
Opis:
In 1959, Nikaidô established a remarkable coincidence theorem in a compact Hausdorff topological space, to generalize and to give a unified treatment to the results of Gale regarding the existence of economic equilibrium and the theorems in game problems. The main purpose of the present paper is to deduce several generalized key results based on this very powerful result, together with some KKM property. Indeed, we shall simplify and reformulate a few coincidence theorems on acyclic multifunctions, as well as some Górniewicz-type fixed point theorems. Beyond the realm of monotonicity nor metrizability, the results derived here generalize and unify various earlier ones from the classic optimization theory. In the sequel, we shall deduce two versions of Nikaidô's coincidence theorem about Vietoris maps from different approaches.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2002, 22, 1; 79-95
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The fixed-point property for deformations of tree-like continua
Autorzy:
Hagopian, Charles
Powiązania:
https://bibliotekanauki.pl/articles/1205393.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
fixed point
arc-component
deformation
tree-like continuum
Borsuk ray
dog-chases-rabbit argument
Opis:
Let f be a map of a tree-like continuum M that sends each arc-component of M into itself. We prove that f has a fixed point. Hence every tree-like continuum has the fixed-point property for deformations (maps that are homotopic to the identity). This result answers a question of Bellamy. Our proof resembles an old argument of Brouwer involving uncountably many tangent curves. The curves used by Brouwer were originally defined by Peano. In place of these curves, we use rays that were originally defined by Borsuk.
Źródło:
Fundamenta Mathematicae; 1998, 155, 2; 161-176
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On spirals and fixed point property
Autorzy:
Mańka, Roman
Powiązania:
https://bibliotekanauki.pl/articles/1208545.pdf
Data publikacji:
1994
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:
We study the famous examples of G. S. Young [7] and R. H. Bing [2]. We generalize and simplify a little their constructions. First we introduce Young spirals which play a basic role in all considerations. We give a construction of a Young spiral which does not have the fixed point property (see Section 5) . Then, using Young spirals, we define two classes of uniquely arcwise connected curves, called Young spaces and Bing spaces. These classes are analogous to the examples mentioned above. The definitions identify the basic distinction between these classes. The main results are Theorems 4.1 and 6.1.
Źródło:
Fundamenta Mathematicae; 1994, 144, 1; 1-9
0016-2736
Pojawia się w:
Fundamenta Mathematicae
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
Wyświetlanie 1-15 z 34

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