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Abstract and Applied Analysis
Volume 2013, Article ID 817392, 6 pages
Research Article

The Problem of Image Recovery by the Metric Projections in Banach Spaces

1Department of Information Science, Toho University, Miyama, Funabashi, Chiba 274-8510, Japan
2Sundai Preparatory School, Kanda-Surugadai, Chiyoda-ku, Tokyo 101-8313, Japan

Received 24 September 2012; Accepted 28 December 2012

Academic Editor: Jaan Janno

Copyright © 2013 Yasunori Kimura and Kazuhide Nakajo. 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.


We consider the problem of image recovery by the metric projections in a real Banach space. For a countable family of nonempty closed convex subsets, we generate an iterative sequence converging weakly to a point in the intersection of these subsets. Our convergence theorems extend the results proved by Bregman and Crombez.