Random fixed points of uniformly Lipschitzian mappings Original Research Article

Let (Ω,Σ) be a measurable space, X a Banach space, C a weakly convex subset of X and T:Ω×C→C a random operator. We prove the random version of a deterministic fixed point theorem when T is an asymptotically nonexpansive mapping and the characteristic of convexity ε0(X) is less than 1. Let N(X) be the normal structure coefficient of X and κ0(X) its Lifschitz constant. If T is k(ω)-uniformly Lipschitzian and there exists a constant c such that View the MathML source we prove that T has a random fixed point.