Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 043796, 9 pages
Random fixed point theorems for multivalued nonexpansive
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
Copyright © 2006 S. Plubtieng and P. Kumam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
be a measurable space, with a
sigma-algebra of subset of , and let
be a nonempty
bounded closed convex separable subset of a Banach space ,
whose characteristic of noncompact convexity is less than 1,
the family of all compact convex subsets of .
We prove that a multivalued nonexpansive non-self-random operator
, 1--contractive mapping,
satisfying an inwardness condition has a random fixed point.