Existence Results for Nonsmooth Vector Quasi-Variational-Like Inequalities

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. (20...

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Published inAbstract and Applied Analysis Vol. 2013; no. 2013; pp. 151 - 157-417
Main Authors Alshahrani, Mohammed, Ansari, Qamrul Hasan, Al-Homidan, Suliman
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2013
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
Hindawi Limited
Wiley
Subjects
Aluminum
Existence theorems
Inequalities
Inequalities (Mathematics)
Mathematical analysis
Mathematical research
Methodology
Theorems
Variational principles
Vector spaces
Vectors (mathematics)
India
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:1085-3375
1687-0409
DOI:10.1155/2013/376829