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  • Research Article
  • Open Access

Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces

Fixed Point Theory and Applications20072007:021972

  • Received: 7 November 2006
  • Accepted: 12 November 2006
  • Published:


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.


  • Banach Space
  • Iterative Method
  • Differential Geometry
  • Nonexpansive Mapping
  • Convex Combination


Authors’ Affiliations

Department of Information Environment, Tokyo Denki University, Muzai Gakuendai, Inzai, Chiba 270-1382, Japan
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-Ku, Tokyo 152-8552, Japan


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© F. Kohsaka and W. Takahashi. 2007

This article is published under license to BioMed Central Ltd. 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.