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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 K C ( C ) has a fixed point. Furthermore, if X is separable then we also prove that a set-valued nonexpansive operator T Ω × C K C ( C ) has a random fixed point.

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