Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 59692, 16 pages
Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces
Department of Mathematics, Kyushu Institute of Technology, Sensuicho, Kitakyushu 804-8550, Tobata, Japan
Received 19 August 2005; Revised 24 February 2006; Accepted 26 February 2006
Copyright © 2006 Tomonari Suzuki. 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 prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let be a bounded closed convex subset of a uniformly smooth Banach space . Let be an infinite family of commuting nonexpansive mappings on . Let and be sequences in satisfying for . Fix and define a sequence in by for . Then converges strongly to , where is the unique sunny nonexpansive retraction from onto .