Journal of Applied Mathematics
Volume 2012 (2012), Article ID 280451, 10 pages
Research Article

Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational Inequalities

1Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan
2Mathematics Department, HITEC University, Texila Cantt, Islamabad, Pakistan

Received 29 March 2012; Accepted 21 April 2012

Academic Editor: Rudong Chen

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.


We introduce and consider a new class of equilibrium problems and variational inequalities involving bifunction, which is called the nonconvex bifunction equilibrium variational inequality. We suggest and analyze some iterative methods for solving the nonconvex bifunction equilibrium variational inequalities using the auxiliary principle technique. We prove that the convergence of implicit method requires only monotonicity. Some special cases are also considered. Our proof of convergence is very simple. Results proved in this paper may stimulate further research in this dynamic field.