Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 805326, 2 pages
Letter to the Editor

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

Department of Mathematics, Hubei Normal University, Huangshi 435002, China

Received 25 September 2009; Accepted 18 January 2010

Copyright © 2010 Shuang Wang. 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.


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 limnβn=1 does not guarantee the strong convergence of the sequence {xn}. In this note, we provide a counter-example to the theorem.