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.
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.