Random approximation with weak contraction random operators and a random fixed point theorem for nonexpansive random self-mappings

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