Journal of Applied Mathematics and Stochastic Analysis 
Volume 2006 (2006), Article ID 43796, 9 pages
doi:10.1155/JAMSA/2006/43796

Random fixed point theorems for multivalued nonexpansive non-self-random operators

S. Plubtieng1 and P. Kumam1

 1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, Bangkok 10140, Thailand
Received 8 March 2005; Revised 9 June 2005; Accepted 4 August 2005

Abstract

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 separable subset of a Banach space X, whose characteristic of noncompact convexity is less than 1, KC(X) the family of all compact convex subsets of X. We prove that a multivalued nonexpansive non-self-random operator T:Ω×C→KC(X), 1-χ-contractive mapping, satisfying an inwardness condition has a random fixed point.