Journal of Applied Mathematics
Volume 2012 (2012), Article ID 691806, 8 pages
Research Article

Explicit Iterative Method for Variational Inequalities on Hadamard Manifolds

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

Received 2 April 2012; Revised 8 May 2012; Accepted 8 May 2012

Academic Editor: Yeong-Cheng Liou

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.


An explicit iterative method for solving the variational inequalities on Hadamard manifold is suggested and analyzed using the auxiliary principle technique. The convergence of this new method requires only the partially relaxed strongly monotonicity, which is a weaker condition than monotonicity. Results can be viewed as refinement and improvement of previously known results.