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.