Journal of Applied Mathematics
Volume 2012 (2012), Article ID 472935, 14 pages
Research Article

Implicit Iterative Method for Hierarchical Variational Inequalities

1Scientific Computing Key Laboratory of Shanghai Universities, Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
3Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
4Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
5Center for General Education, Kaohsiung Medical University, Kaohsiung 80708, Taiwan

Received 1 February 2012; Accepted 10 February 2012

Academic Editor: Yonghong Yao

Copyright © 2012 L.-C. Ceng 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 introduce a new implicit iterative scheme with perturbation for finding the approximate solutions of a hierarchical variational inequality, that is, a variational inequality over the common fixed point set of a finite family of nonexpansive mappings. We establish some convergence theorems for the sequence generated by the proposed implicit iterative scheme. In particular, necessary and sufficient conditions for the strong convergence of the sequence are obtained.