Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 583082, 19 pages
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

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

Received 2 July 2008; Accepted 23 December 2008

Academic Editor: Hichem Ben-El-Mechaiekh

Copyright © 2008 Somyot Plubtieng and Kasamsuk Ungchittrakool. 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.


The convex feasibility problem (CFP) of finding a point in the nonempty intersection i=1NCi is considered, where N1 is an integer and the Ci's are assumed to be convex closed subsets of a Banach space E. 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.