Random fixed point theorem for multivalued nonexpansive operators in Uniformly nonsquare Banach spaces
Poom Kumam, Somyot Plubtieng · Random Operators and Stochastic Equations · 2006
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.