WEAK CONVERGENCE OF PERTURBED MANN ITERATION FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

Abstract

In this paper, we adapt three different forms of Mann iteration algorithm with appropriate small perturbation to prove the robustness of Mann iteration algorithms for asymptotically nonexpansive mappings, that is, appropriate small perturbation do not alter the weak convergenc of Mann iteration processes. The results of this paper extend the recent work of Kim and Xu from nonexpansive mappings to asymptotically nonexpansive mappings.