Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 649162, 9 pages
Research Article

Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings

Liang-Gen Hu

Department of Mathematics, Ningbo University, Ningbo 315211, China

Received 12 September 2008; Accepted 9 December 2008

Academic Editor: Jerzy Jezierski

Copyright © 2008 Liang-Gen Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The purpose of this paper is to consider that a modified Halpern's iterative sequence {xn} converges strongly to a fixed point of nonexpansive mappings in Banach spaces which have a uniformly Gâteaux differentiable norm. Our result is an extension of the corresponding results.