Open Access

Hybrid Iterative Methods for Convex Feasibility Problems and Fixed Point Problems of Relatively Nonexpansive Mappings in Banach Spaces

Fixed Point Theory and Applications20092008:583082

https://doi.org/10.1155/2008/583082

Received: 2 July 2008

Accepted: 23 December 2008

Published: 20 January 2009

Abstract

The convex feasibility problem (CFP) of finding a point in the nonempty intersection is considered, where is an integer and the 's are assumed to be convex closed subsets of a Banach space . By using hybrid iterative methods, we prove theorems on the strong convergence to a common fixed point for a finite family of relatively nonexpansive mappings. Then, we apply our results for solving convex feasibility problems in Banach spaces.

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Authors’ Affiliations

(1)
Department of Mathematics, Faculty of Science, Naresuan University

Copyright

© S. Plubtieng and K. Ungchittrakool. 2008

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.