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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 907105, 19 pages
http://dx.doi.org/10.1155/2012/907105
Research Article

Hybrid Steepest Descent Viscosity Method for Triple Hierarchical Variational Inequalities

1Department of Mathematics, Shanghai Normal University and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China
2Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
3Center for General Education, Kaohsiung Medical University, Kaohsiung 80708, Taiwan

Received 21 June 2012; Accepted 26 July 2012

Academic Editor: Jen-Chih 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.

Abstract

We consider a triple hierarchical variational inequality problem (in short, THVIP). By combining hybrid steepest descent method, viscosity method, and projection method, we propose an approximation method to compute the approximate solution of THVIP. We also study the strong convergence of the sequences generated by the proposed method to a solution of THVIP.