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Journal of Applied Mathematics
Volume 2012, Article ID 646259, 10 pages
Research Article

Implicit Schemes for Solving Extended General Nonconvex Variational Inequalities

1Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan
2Mathematics Department, Nanjing University, Nanjing 210093, China
3Mathematics Department, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

Received 2 November 2011; Accepted 14 November 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.


We suggest and analyze some implicit iterative methods for solving the extended general nonconvex variational inequalities using the projection technique. We show that the convergence of these iterative methods requires only the gh-pseudomonotonicity, which is a weaker condition than gh-monotonicity. We also discuss several special cases. Our method of proof is very simple as compared with other techniques.