The characteristic of noncompact convexity and random fixed point theorem for set-valued operators |
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| Authors: | Poom Kumam Somyot Plubtieng |
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| Institution: | (1) Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok, 10140, Thailand;(2) Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand |
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| Abstract: | 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, KC(C) the family of all compact convex subsets of C. We prove that a set-valued nonexpansive mapping T: C → KC(C) has a fixed point. Furthermore, if X is separable then we also prove that a set-valued nonexpansive operator T: Ω × C → KC(C) has a random fixed point. |
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| Keywords: | random fixed point set-valued random operator measure of noncompactness |
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