Poom KUMAM, Somyot PLUBTIENG

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

Let (W, S) be a measurable space, with \sum a sigma-algebra of subsets of W, 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: W \times E \rightarrow KC(X) satisfying an inwardness condition and itself being a 1-c-contractive nonexpansive mapping has a random fixed point. We also prove that a multivalued nonexpansive, non-self operator T:W\times E\rightarrow KC(X) with a uniformly convex X satisfying an inwardness condition has a random fixed point.

Anahtar Kelimeler:

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

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

Keywords:

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

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Department of Mathematics King Mongkut’s University of Technology Bangkok 10140 THAILAND e-mail: poom.kum@kmutt.ac.th Somyot PLUBTIENG
Department of Mathematics, Naresuan University, Pitsanulok 65000. THAILAND e-mail: Somyotp@nu.ac.th.