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Open Access Research Article

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

Liang-Gen Hu

Author Affiliations

Department of Mathematics, Ningbo University, Ningbo 315211, China

Fixed Point Theory and Applications 2008, 2008:649162  doi:10.1155/2008/649162

The electronic version of this article is the complete one and can be found online at: http://www.fixedpointtheoryandapplications.com/content/2008/1/649162


Received:12 September 2008
Accepted:9 December 2008
Published:21 December 2008

© 2008 The Author(s).

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.

Abstract

The purpose of this paper is to consider that a modified Halpern's iterative sequence 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.

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