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The characteristic of noncompact convexity and random fixed point theorem for set-valued operators

Poom Kumam, Somyot Plubtieng (2007)

Czechoslovak Mathematical Journal

Let $(Ω, Σ)$ be a measurable space, $X$ a Banach space whose characteristic of noncompact convexity is less than 1, $C$ a bounded closed convex subset of $X$ , $K C (C)$ the family of all compact convex subsets of $C .$ We prove that a set-valued nonexpansive mapping $T C \to K C (C)$ has a fixed point. Furthermore, if $X$ is separable then we also prove that a set-valued nonexpansive operator $T Ω \times C \to K C (C)$ has a random fixed point.

The dual form of Knaster-Kuratowski-Mazurkiewicz principle in hyperconvex metric spaces and some applications

George Isac, George Xian-Zhi Yuan (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we first establish the dual form of Knaster- Kuratowski-Mazurkiewicz principle which is a hyperconvex version of corresponding result due to Shih. Then Ky Fan type matching theorems for finitely closed and open covers are given. As applications, we establish some intersection theorems which are hyperconvex versions of corresponding results due to Alexandroff and Pasynkoff, Fan, Klee, Horvath and Lassonde. Then Ky Fan type best approximation theorem and Schauder-Tychonoff fixed point...

The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity

Jarosław L. Bojarski (2005)

Applicationes Mathematicae

The aim of this paper is to study the unilateral contact condition (Signorini problem) for polyconvex functionals with linear growth at infinity. We find the lower semicontinuous relaxation of the original functional (defined over a subset of the space of bounded variations BV(Ω)) and we prove the existence theorem. Moreover, we discuss the Winkler unilateral contact condition. As an application, we show a few examples of elastic-plastic potentials for finite displacements.

The theory of Reich's fixed point theorem for multivalued operators.

Lazăr, Tania, Moţ, Ghiocel, Petruşel, Gabriela, Szentesi, Silviu (2010)

Fixed Point Theory and Applications [electronic only]

The von Neumann minimax theorem revisited

Hichem Ben-El-Mechaiekh, Robert Dimand (2007)

Banach Center Publications

Topological and approximation methods of degree theory of set-valued maps [Book]

Wojciech Kryszewski (1994)

Topological entropy and differential equations

Ján Andres, Pavel Ludvík (2023)

Archivum Mathematicum

On the background of a brief survey panorama of results on the topic in the title, one new theorem is presented concerning a positive topological entropy (i.e. topological chaos) for the impulsive differential equations on the Cartesian product of compact intervals, which is positively invariant under the composition of the associated Poincaré translation operator with a multivalued upper semicontinuous impulsive mapping.

Topological essentiality for multivalued weighted mappings

Robert Skiba (2002)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Transfer positive hemicontinuity and zeros, coincidences, and fixed points of maps in topological vector spaces.

Włodarczyk, K., Klim, D. (2005)

Fixed Point Theory and Applications [electronic only]

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