Displaying similar documents to “Random fixed point theorems for multivalued nonexpansive non-self-random operators.”

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

Poom Kumam, Somyot Plubtieng (2007)

Czechoslovak Mathematical Journal

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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.

Metric fixed point theory for multivalued mappings

Hong-Kun Xu

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Some new and recent results on the fixed point theory of multivalued contractions and nonexpansive mappings are presented. Discussions concerning Reich's problem are included. Existence of fixed points for weakly inward contractions is proved. Local contractions are also discussed. The Kirk-Massa theorem is extended to inward multivalued nonexpansive mappings. Using an inequality characteristic of uniform convexity, another proof of Lim's theorem on weakly inward multivalued nonexpansive...