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

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.