Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 583423, 10 pages
doi:10.1155/2011/583423
Research Article

Strong Convergence Theorems for Lipschitzian Demicontraction Semigroups in Banach Spaces

Shih-sen Chang,1 Yeol Je Cho,2 H. W. Joseph Lee,3 and Chi Kin Chan3

1Department of Mathematics, Yibin University, Yibin, Sichuan 644007, China
2Department of Mathematics Education and RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea
3Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong

Received 24 November 2010; Accepted 9 February 2011

Academic Editor: Jong Kyu Kim

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 introduce and study the strong convergence problem of the explicit iteration process for a Lipschitzian and demicontraction semigroups in arbitrary Banach spaces. The main results presented in this paper not only extend and improve some recent results announced by many authors, but also give an affirmative answer for the open questions raised by Suzuki (2003) and Xu (2005).