Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 936121, 16 pages
doi:10.1155/2009/936121
Research Article

Viscosity Approximation of Common Fixed Points for L-Lipschitzian Semigroup of Pseudocontractive Mappings in Banach Spaces

Xue-song Li,1 Jong Kyu Kim,2 and Nan-jing Huang1

1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2Department of Mathematics, Kyungnam University, Masan, Kyungnam 631-701, South Korea

Received 14 January 2009; Accepted 5 March 2009

Academic Editor: Charles E. Chidume

Copyright © 2009 Xue-song Li 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

We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach spaces satisfying some conditions. The results presented in this paper extend and generalize some results concerned with the nonexpansive semigroup in (Chen and He, 2007) and the pseudocontractive mapping in (Zegeye et al., 2007) to the pseudocontractive semigroup in Banach spaces under different conditions.