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.

Abstract

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.