Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 869458, 11 pages
doi:10.1155/2011/869458
Research Article

Strong Convergence of Modified Halpern Iterations in CAT(0) Spaces

A. Cuntavepanit1 and B. Panyanak1,2

1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2Materials Science Research Center, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received 28 November 2010; Accepted 10 January 2011

Academic Editor: Qamrul Hasan Ansari

Copyright © 2011 A. Cuntavepanit and B. Panyanak. 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

Strong convergence theorems are established for the modified Halpern iterations of nonexpansive mappings in CAT(0) spaces. Our results extend and improve the recent ones announced by Kim and Xu (2005), Hu (2008), Song and Chen (2008), Saejung (2010), and many others.