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.

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