A new composite implicit iterative algorithm for nonself asymptotically nonexpansive mappings

Abstract

Let E be a real uniformly convex and smooth Banach space with P as a sunny nonexpansive retraction, K be a nonempty closed convex subset of E. Let {Si}i=1N, {Ti}i=1N:K→K be two finite families of weakly inward and asymptotically nonexpansive mappings with respect to P. It is proved that the composite implicit iteration process converges weakly and strongly to a common fixed point of {Si}i=1N, {Ti}i=1N under certain conditions. The results of this paper improve and extend some well known corresponding results.