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Open Access Research Article

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

Somyot Plubtieng* and Kasamsuk Ungchittrakool

Author Affiliations

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

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Fixed Point Theory and Applications 2008, 2008:583082  doi:10.1155/2008/583082

The electronic version of this article is the complete one and can be found online at: http://www.fixedpointtheoryandapplications.com/content/2008/1/583082


Received:2 July 2008
Accepted:23 December 2008
Published:20 January 2009

© 2008 The Author(s).

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

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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