International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 174796, 31 pages
http://dx.doi.org/10.1155/2011/174796
Research Article

Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems

Kriengsak Wattanawitoon1,2 and Poom Kumam2,3

1Department of Mathematics and Statistics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Tak, Tak 63000, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayuthaya Road, Bangkok 10400, Thailand
3Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bang Mod, Bangkok 10140, Thailand

Received 15 November 2010; Accepted 29 December 2010

Academic Editor: Yonghong Yao

Copyright © 2011 Kriengsak Wattanawitoon and Poom Kumam. 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 prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the variational inequality operators of an inverse strongly monotone in a Banach space under different conditions. Moreover, applications to complementarity problems are given. Our results modify and improve the recently announced ones by Li and Song (2008) and many authors.