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
Fixed Point Theory and Applications 2004, 2004:829453 doi:10.1155/S1687182004310089Published: 3 March 2004
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.