Open Access

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

Fixed Point Theory and Applications20102010:805326

DOI: 10.1155/2010/805326

Received: 25 September 2009

Accepted: 18 January 2010

Published: 20 January 2010

Abstract

In the paper by Hu in 2008, the author proved a strong convergence result for nonexpansive mappings using a modified Halpern's iteration algorithm. Unfortunately, the case does not guarantee the strong convergence of the sequence . In this note, we provide a counter-example to the theorem.

Publisher note

To access the full article, please see PDF

Authors’ Affiliations

(1)
Department of Mathematics, Hubei Normal University

Copyright

© Shuang Wang. 2010

This article is published under license to BioMed Central Ltd. 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.