Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 471781, 13 pages
doi:10.1155/2010/471781
Research Article

Halpern's Iteration in CAT(0) Spaces

Satit Saejung1,2

1Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2Centre of Excellence in Mathematics, CHE, Sriayudthaya Road, Bangkok 10400, Thailand

Received 26 September 2009; Accepted 24 November 2009

Academic Editor: Mohamed A. Khamsi

Copyright © 2010 Satit Saejung. 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

Motivated by Halpern's result, we prove strong convergence theorem of an iterative sequence in CAT(0) spaces. We apply our result to find a common fixed point of a family of nonexpansive mappings. A convergence theorem for nonself mappings is also discussed.