Fixed Point Theory and Applications
Volume 2004 (2004), Issue 1, Pages 37-47
Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152-8552, Japan
Received 29 October 2003
Copyright © 2004 Shin-ya Matsushita and Wataru Takahashi. 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 first introduce an iterative sequence for finding fixed points
of relatively nonexpansive mappings in Banach spaces, and then
prove weak and strong convergence theorems by using the notion of
generalized projection. We apply these results to the convex
feasibility problem and a proximal-type algorithm for monotone
operators in Banach spaces.