Journal of Applied Mathematics
Volume 2012 (2012), Article ID 804538, 16 pages
http://dx.doi.org/10.1155/2012/804538
Research Article

Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems

Kamonrat Nammanee,1 Suthep Suantai,2,3 and Prasit Cholamjiak1,3

1School of Science, University of Phayao, Phayao 56000, Thailand
2Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
3Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 13 February 2012; Accepted 9 March 2012

Academic Editor: Rudong Chen

Copyright © 2012 Kamonrat Nammanee et al. 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

We introduce hybrid-iterative schemes for solving a system of the zero-finding problems of maximal monotone operators, the equilibrium problem, and the fixed point problem of weak relatively nonexpansive mappings. We then prove, in a uniformly smooth and uniformly convex Banach space, strong convergence theorems by using a shrinking projection method. We finally apply the obtained results to a system of convex minimization problems.