A RANDOM FIXED-POINT THEOREM FOR MULTIVALUED NONEXPANSIVE OPERATORS IN UNIFORMLY CONVEX BANACH-SPACES

Let (OMEGA, SIGMA) be a measurable space with SIGMA a sigma-algebra of subsets of OMEGA, and let C be a nonempty, bounded, closed, convex, and separable subset of a uniformly convex Banach space X. It is shown that every multivalued nonexpansive random operator T: OMEGA x C --> K(C) has a random fixed point, where K(C) is the family of all nonempty compact subsets of C endowed with the Hausdorff metric induced by the norm of X.