Convergence Theorems of a New Three-Step Iteration for Nonself Asymptotically Nonexpansive Mappings

Birol Gunduz, Sezgin Akbulut

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 T_{i}:K→E (i=1,2,3) be three of weakly inward and nonself asymptotically nonexpansive mappings with respect to P. It is proved that three step iteration converges weakly and strongly to a common fixed point of T_{i} (i=1,2,3) under certain conditions. It presents some new results in this paper.