Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 805326, 2 pages
doi:10.1155/2010/805326

A note on strong convergence of a modified Halpern's iteration for nonexpansive mappings

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.