Fixed Point Theory and Applications 
Volume 2004 (2004), Issue 1, Pages 37-47
doi:10.1155/S1687182004310089

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

Abstract

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.