Journal of Applied Mathematics
Volume 2012 (2012), Article ID 125373, 10 pages
http://dx.doi.org/10.1155/2012/125373
Research Article

Iterative Schemes for a Class of Mixed Trifunction Variational Inequalities

Muhammad Aslam Noor,1,2 Khalida Inayat Noor,1 and Eisa Al-Said2

1Mathematics Department, COMSATS University of Science and Technology, Park Road, Islamabad, Pakistan
2Mathematics Department, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

Received 30 September 2011; Accepted 21 October 2011

Academic Editor: Yonghong Yao

Copyright © 2012 Muhammad Aslam Noor 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 use the auxiliary principle technique to suggest and analyze some iterative methods for solving a new class of variational inequalities, which is called the mixed trifunction variational inequality. The mixed trifunction variational inequality includes the trifunction variational inequalities and the classical variational inequalities as special cases. Convergence of these iterative methods is proved under very mild and suitable assumptions. Several special cases are also considered. Results proved in this paper continue to hold for these known and new classes of variational inequalities and its variant forms.