Journal of Applied Mathematics
Volume 2012 (2012), Article ID 412413, 7 pages
http://dx.doi.org/10.1155/2012/412413
Research Article

On New Proximal Point Methods for Solving the Variational Inequalities

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

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

Received 3 October 2011; Accepted 19 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

It is well known that the variational inequalities are equivalent to the fixed point problem. We use this alternative equivalent formulation to suggest and analyze some new proximal point methods for solving the variational inequalities. These new methods include the explicit, the implicit, and the extragradient methods as special cases. The convergence analysis of the new methods is considered under some suitable conditions. Results proved in this paper may stimulate further research in this direction.