International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 687815, 10 pages
Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
Received 13 May 2008; Accepted 14 August 2008
Academic Editor: Nils Ackermann
Copyright © 2008 Yali 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.
Let be a nonempty closed convex subset of a reflexive and strictly convex Banach
space with a uniformly Gâteaux differentiable norm, a generalized asymptotically
nonexpansive self-mapping semigroup of , and a fixed contractive mapping
with contractive coefficient . We prove that the following implicit and modified implicit
viscosity iterative schemes defined by and strongly converge to as and is the unique solution to the following variational
inequality: for all .