Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 680930, 11 pages
doi:10.1155/2011/680930
Research Article

On the Convergence Theorems for a Countable Family of Lipschitzian Pseudocontraction Mappings in Banach Spaces

Shih-sen Chang,1 Jong Kyu Kim,2 H. W. Joseph Lee,3 and Chi Kin Chan3

1Department of Mathematics, Yibin University, Yibin, Sichuan 644007, China
2Department of Mathematics Education, Kyungnam University, Masan, Kyungnam 631-701, Republic of Korea
3Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received 26 October 2010; Revised 2 December 2010; Accepted 16 December 2010

Academic Editor: Yeol J. E. Cho

Copyright © 2011 Shih-sen Chang et al. 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

The purpose of this paper is to study the weak and strong convergence theorems of the implicit iteration process for a countable family of Lipschitzian pseudocontraction mappings in Banach spaces. The results presented in this paper extend and improve some recent results announced by some authors.