<p>Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces</p>

1687-1812-2004-829453 1687-1812 Research Article <p>Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces</p> MatsushitaShin-yashinya2@is.titech.ac.jp TakahashiWataruwataru@is.titech.ac.jp

Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152-8552, Japan

Fixed Point Theory and Applications 1687-1812 2004 2004 1 829453 http://www.fixedpointtheoryandapplications.com/content/2004/1/829453 10.1155/S1687182004310089 29102003332004 2004Matsushita and Takahashi

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.