Mann and Ishikawa iterations with errors for asymptotically nonexpansive mappings

Abstract

In a recent paper, Rhoades [1] presented some generalizations of Schu [2] on the convergence of the Mann and Ishikawa iterations of asymptotically nonexpansive mappings in uniformly convex Banach spaces. We continue the study on the Ishikawa (and Mann) iteration process with errors and prove that if X is a uniformly convex Banach space, ø ≠ E ⊂ X closed bounded and convex, and T : E → E is an asymptotically nonexpansive mapping, then the Ishikawa (and Mann) iteration process with errors converges strongly to some fixed point of T.