Some Random Fixed Point Theorems for Non-Self Nonexpansive Random Operators

Authors: POOM KUMAM, SOMYOT PLUBTIENG

Abstract: Let (\Omega, \Sigma) be a measurable space, with \sum a sigma-algebra of subsets of \Omega, and let E be a nonempty bounded closed convex and separable subset of a Banach space X, whose characteristic of noncompact convexity is less than 1. We prove that a multivalued nonexpansive, non-self operator T: \Omega \times E \rightarrow KC(X) satisfying an inwardness condition and itself being a 1-\chi-contractive nonexpansive mapping has a random fixed point. We also prove that a multivalued nonexpansive, non-self operator T:\Omega\times E\rightarrow KC(X) with a uniformly convex X satisfying an inwardness condition has a random fixed point.

Keywords: Random fixed point, non-self mappings, Nonexpansive random operator, inwardness condition

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