Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 21972, 18 pages
doi:10.1155/2007/21972
Research Article
Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces
1Department of Information Environment, Tokyo Denki University, Muzai Gakuendai, Inzai 270-1382, Chiba, Japan
2Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-Ku 152-8552, Tokyo, Japan
Received 7 November 2006; Accepted 12 November 2006
Academic Editor: Ravi P. Agarwal
Copyright © 2007 Fumiaki Kohsaka 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.
Abstract
Using the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of the mappings. Next, using this operator, we construct an iterative sequence to approximate common fixed points of the family. We finally apply our results to a convex feasibility problem in Banach spaces.