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

• Volume: 57, Issue: 1, page 269-279
• ISSN: 0011-4642

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## Abstract

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Let $\left(\Omega ,\Sigma \right)$ be a measurable space, $X$ a Banach space whose characteristic of noncompact convexity is less than 1, $C$ a bounded closed convex subset of $X$, $KC\left(C\right)$ the family of all compact convex subsets of $C.$ We prove that a set-valued nonexpansive mapping $T\phantom{\rule{0.222222em}{0ex}}C\to KC\left(C\right)$ has a fixed point. Furthermore, if $X$ is separable then we also prove that a set-valued nonexpansive operator $T\phantom{\rule{0.222222em}{0ex}}\Omega ×C\to KC\left(C\right)$ has a random fixed point.

## How to cite

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Kumam, Poom, and Plubtieng, Somyot. "The characteristic of noncompact convexity and random fixed point theorem for set-valued operators." Czechoslovak Mathematical Journal 57.1 (2007): 269-279. <http://eudml.org/doc/31129>.

@article{Kumam2007,
abstract = {Let $(\Omega ,\Sigma )$ be a measurable space, $X$ a Banach space whose characteristic of noncompact convexity is less than 1, $C$ a bounded closed convex subset of $X$, $KC(C)$ the family of all compact convex subsets of $C.$ We prove that a set-valued nonexpansive mapping $T\: C\rightarrow KC(C)$ has a fixed point. Furthermore, if $X$ is separable then we also prove that a set-valued nonexpansive operator $T\: \Omega \times C\rightarrow KC(C)$ has a random fixed point.},
author = {Kumam, Poom, Plubtieng, Somyot},
journal = {Czechoslovak Mathematical Journal},
keywords = {random fixed point; set-valued random operator; measure of noncompactness; random fixed point; set-valued random operator; measure of noncompactness},
language = {eng},
number = {1},
pages = {269-279},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The characteristic of noncompact convexity and random fixed point theorem for set-valued operators},
url = {http://eudml.org/doc/31129},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Kumam, Poom
AU - Plubtieng, Somyot
TI - The characteristic of noncompact convexity and random fixed point theorem for set-valued operators
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 269
EP - 279
AB - Let $(\Omega ,\Sigma )$ be a measurable space, $X$ a Banach space whose characteristic of noncompact convexity is less than 1, $C$ a bounded closed convex subset of $X$, $KC(C)$ the family of all compact convex subsets of $C.$ We prove that a set-valued nonexpansive mapping $T\: C\rightarrow KC(C)$ has a fixed point. Furthermore, if $X$ is separable then we also prove that a set-valued nonexpansive operator $T\: \Omega \times C\rightarrow KC(C)$ has a random fixed point.
LA - eng
KW - random fixed point; set-valued random operator; measure of noncompactness; random fixed point; set-valued random operator; measure of noncompactness
UR - http://eudml.org/doc/31129
ER -

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