International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 16470, 12 pages
Strong convergence of approximation fixed points for nonexpansive
Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
Received 17 May 2006; Accepted 22 June 2006
Copyright © 2006 Rudong Chen and Zhichuan Zhu. 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 closed convex subset of a uniformly smooth Banach
space , and a nonexpansive nonself-mapping satisfying the weakly inwardness condition such that , and a fixed contractive mapping. For , the implicit iterative sequence is defined by , the explicit iterative sequence is given by , where and is a sunny nonexpansive retraction of onto .
We prove that strongly converges to a fixed point of
as , and strongly converges to a fixed point of as satisfying appropriate conditions. The results presented extend and improve the corresponding results of Hong-Kun Xu (2004) and Yisheng Song and Rudong Chen (2006).