New Fixed Point Iterations with Errors for Nonexpansive Nonself-Mapping

Abstract

In this paper, a new type of two-step iteration with errors for a nonexpansive nonself-mapping is introduced and studied. Weak and strong convergence theorems of such iterations are established under certain conditions in a uniformly convex Banach space. The results obtained in this paper extend and improve the corresponding results of Shahzad [N. Shahzad,  Approximating fixed points of non-self nonexpansive mappings in Banach spaces, Nonlinear Anal., 61(2005), 1031–1039], Tan and Xu [K.K. Tan and H.K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., 178(1993), 301–308] and others.