Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 579725, 21 pages
Research Article

Strong Convergence Theorems of Viscosity Iterative Methods for a Countable Family of Strict Pseudo-contractions in Banach Spaces

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 23 June 2010; Accepted 13 August 2010

Academic Editor: A. T. M. Lau

Copyright © 2010 Rabian Wangkeeree and Uthai Kamraksa. 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.


For a countable family {Tn}n=1 of strictly pseudo-contractions, a strong convergence of viscosity iteration is shown in order to find a common fixed point of {Tn}n=1 in either a p-uniformly convex Banach space which admits a weakly continuous duality mapping or a p-uniformly convex Banach space with uniformly Gâteaux differentiable norm. As applications, at the end of the paper we apply our results to the problem of finding a zero of accretive operators. The main result extends various results existing in the current literature.