Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 583082, 19 pages
doi:10.1155/2008/583082
Research Article
Hybrid Iterative Methods for Convex Feasibility Problems and Fixed Point Problems of Relatively Nonexpansive Mappings in Banach Spaces
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.
Abstract
The convex feasibility problem (CFP) of finding a point in the nonempty intersection
⋂i=1NCi is considered, where N⩾1 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.