Existence Results for Nonsmooth Vector Quasi-Variational-Like Inequalities. (24th September 2013)

• Record Type: Journal Article
• Authors: Alshahrani, Mohammed; Ansari, Qamrul Hasan; Al-Homidan, Suliman
• Other Names: Yao Jen-Chih Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-09-24
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/376829
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : 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.