Random Approximation with Weak Contraction Random Operator and Random Fixed Point Theorem for Nonexpansive Random Mapping

In real reflexive separable Banach space which admits a weakly sequentially continuous duality mapping, the sufficient and necessary condition that nonexpansive random mapping has a random fixed point is obtained. By introducing a random iteration process with weak contraction random operator, we obtain the convergence theorem of the random iteration process to a random fixed point for nonexpansive random mapping.