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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 610852, 9 pages
http://dx.doi.org/10.1155/2012/610852
Research Article

Some Proximal Methods for Solving Mixed Variational Inequalities

1Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan
2Department of Mathematics, Nanjing University, Nanjing 210093, China

Received 15 February 2012; Accepted 28 February 2012

Academic Editor: Khalida Inayat Noor

Copyright © 2012 Muhammad Aslam Noor and Zhenyu Huang. 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 mixed variational inequalities are equivalent to the fixed point problem. We use this alternative equivalent formulation to suggest some new proximal point methods for solving the mixed variational inequalities. These new methods include the explicit, the implicit, and the extragradient method as special cases. The convergence analysis of these new methods is considered under some suitable conditions. Our method of constructing these iterative methods is very simple. Results proved in this paper may stimulate further research in this direction.