Journal of Applied Mathematics
Volume 2012 (2012), Article ID 437391, 9 pages
http://dx.doi.org/10.1155/2012/437391
Research Article

Implicit Methods for Equilibrium Problems on Hadamard Manifolds

Muhammad Aslam Noor,1 Saira Zainab,2 and Yonghong Yao3

1Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan
2Mathematics Department, HITEC University, Taxila Cantt, Pakistan
3Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China

Received 26 March 2012; Accepted 3 April 2012

Academic Editor: Rudong Chen

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

We use the auxiliary principle technique to suggest and analyze an implicit method for solving the equilibrium problems on Hadamard manifolds. The convergence of this new implicit method requires only the speudomonotonicity, which is a weaker condition than monotonicity. Some special cases are also considered.