Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 262691, 12 pages
doi:10.1155/2010/262691
Research Article

A New General Iterative Method for a Finite Family of Nonexpansive Mappings in Hilbert Spaces

Urailuk Singthong1 and Suthep Suantai1,2

1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2PERDO National Centre of Excellence in Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand

Received 10 February 2010; Revised 21 June 2010; Accepted 15 July 2010

Academic Editor: Massimo Furi

Copyright © 2010 Urailuk Singthong and Suthep Suantai. 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 introduce a new general iterative method by using the K-mapping for finding a common fixed point of a finite family of nonexpansive mappings in the framework of Hilbert spaces. A strong convergence theorem of the purposed iterative method is established under some certain control conditions. Our results improve and extend the results announced by many others.