Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 301868, 15 pages
doi:10.1155/2010/301868
Research Article

Strong Convergence to Common Fixed Points for Countable Families of Asymptotically Nonexpansive Mappings and Semigroups

Kriengsak Wattanawitoon1,2 and Poom Kumam2,3

1Department of Mathematics and Statistics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Tak, Tak 63000, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayuthaya Road, Bangkok 10400, Thailand
3Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Thrungkru, Bangkok 10140, Thailand

Received 15 April 2010; Accepted 11 October 2010

Academic Editor: A. T. M. Lau

Copyright © 2010 Kriengsak Wattanawitoon and Poom Kumam. 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

We prove strong convergence theorems for countable families of asymptotically nonexpansive mappings and semigroups in Hilbert spaces. Our results extend and improve the recent results of Nakajo and Takahashi (2003) and of Zegeye and Shahzad (2008) from the class of nonexpansive mappings to asymptotically nonexpansive mappings.