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Journal of Applied Mathematics
Volume 2012, Article ID 657278, 8 pages
http://dx.doi.org/10.1155/2012/657278
Research Article

Proximal Point Methods for Solving Mixed Variational Inequalities on the Hadamard Manifolds

Mathematics Department, COMSATS Institute of Information Technology, Islamabad 44000, Pakistan

Received 21 March 2012; Accepted 28 March 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Muhammad Aslam Noor and Khalida Inayat Noor. 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 a proximal point method for solving the mixed variational inequalities on the Hadamard manifold. It is shown that the convergence of this proximal point method needs only pseudomonotonicity, which is a weaker condition than monotonicity. Some special cases are also considered. Results can be viewed as refinement and improvement of previously known results.