Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 632137, 16 pages
doi:10.1155/2010/632137
Research Article

Weak Convergence Theorems for a Countable Family of Strict Pseudocontractions in Banach Spaces

Prasit Cholamjiak1 and Suthep Suantai1,2

1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 2 June 2010; Accepted 16 September 2010

Academic Editor: Massimo Furi

Copyright © 2010 Prasit Cholamjiak 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 investigate the convergence of Mann-type iterative scheme for a countable family of strict pseudocontractions in a uniformly convex Banach space with the Fréchet differentiable norm. Our results improve and extend the results obtained by Marino-Xu, Zhou, Osilike-Udomene, Zhang-Guo and the corresponding results. We also point out that the condition given by Chidume-Shahzad (2010) is not satisfied in a real Hilbert space. We show that their results still are true under a new condition.