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

Shin-ya Matsushita and Wataru Takahashi

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.