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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 376829, 7 pages
Research Article

Existence Results for Nonsmooth Vector Quasi-Variational-Like Inequalities

1Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
2Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India

Received 27 June 2013; Accepted 1 August 2013

Academic Editor: Jen-Chih Yao

Copyright © 2013 Mohammed Alshahrani 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 nonsmooth vector quasi-variational-like inequalities (NVQVLI) by means of a bifunction. We establish some existence results for solutions of these inequalities by using Fan-KKM theorem and a maximal element theorem. By using the technique and methodology adopted in Al-Homidan et al. (2012), one can easily derive the relations among these inequalities and a vector quasi-optimization problem. Hence, the existence results for a solution of a vector quasi-optimization problem can be derived by using our results. The results of this paper extend several known results in the literature.