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Poom Kumam, Somyot Plubtieng

Random fixed point theorem for multivalued nonexpansive operators in Uniformly nonsquare Banach spaces

Keywords: Random fixed point, multivalued mappings, inwardness condition, Dominguez-Lorenzo condition, WORTH, Opial condition, uniformly nonsquare

Let (Ω, Σ) be a measurable space, with Σ a sigma-algebra of subset of Ω, and let C be a nonempty bounded closed convex and separable subset of a Banach space X, satisfying Dominguez-Lorenzo condition, KC(X) the family of all compact convex subsets of X . We prove that a 1 _-χ contractive mutivalued nonexpansive random operator from C into KC(X ) satisfying an inwardness condition has a random fixed point. Furthermore, we also prove that a uniformly nonsquare Banach spaces with property WORTH has a random fixed point for multivalued nonexpansive non-self random operators.

Random Operators and Stochastic Equations, Walter de Gruyter

Print ISSN: 0926-6364
Volume: 14, 03/2006
Pages: 35 - 44

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