Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 689478, 17 pages
doi:10.1155/2011/689478
Research Article

System of General Variational Inequalities Involving Different Nonlinear Operators Related to Fixed Point Problems and Its Applications

Issara Inchan1,2 and Narin Petrot2,3

1Department of Mathematics and computer, Faculty of Science and Technology, Uttaradit Rajabhat University, Uttaradit 53000, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
3Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 5 October 2010; Revised 11 November 2010; Accepted 9 December 2010

Academic Editor: Qamrul Hasan Ansari

Copyright © 2011 Issara Inchan and Narin Petrot. 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

By using the projection methods, we suggest and analyze the iterative schemes for finding the approximation solvability of a system of general variational inequalities involving different nonlinear operators in the framework of Hilbert spaces. Moreover, such solutions are also fixed points of a Lipschitz mapping. Some interesting cases and examples of applying the main results are discussed and showed. The results presented in this paper are more general and include many previously known results as special cases.