Journal of Applied Mathematics
Volume 2012, Article ID 641479, 19 pages
http://dx.doi.org/10.1155/2012/641479
Strong Convergence Theorems for Nonexpansive Semigroups and Variational Inequalities in Banach Spaces
1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
2Department of Mathematics, Tianjin No. 8 Middle School, Tianjin 300252, China
Received 11 November 2011; Accepted 17 December 2011
Academic Editor: Rudong Chen
Copyright © 2012 Haiqing Wang 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
Let be a uniformly convex Banach space and be a nonexpansive semigroup such that . Consider the iterative method that generates the sequence by the algorithm , where , , and are three sequences satisfying certain conditions, is a contraction mapping. Strong convergence of the algorithm is proved assuming either has a weakly continuous duality map or has a uniformly Gâteaux differentiable norm.