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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/376829 |
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| author | Mohammed Alshahrani Qamrul Hasan Ansari Suliman Al-Homidan |
| author_facet | Mohammed Alshahrani Qamrul Hasan Ansari Suliman Al-Homidan |
| author_sort | Mohammed Alshahrani |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-403f89b0086a4ecdacc8722313cb3453 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-403f89b0086a4ecdacc8722313cb34532025-02-03T05:46:25ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/376829376829Existence Results for Nonsmooth Vector Quasi-Variational-Like InequalitiesMohammed Alshahrani0Qamrul Hasan Ansari1Suliman Al-Homidan2Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi ArabiaDepartment of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi ArabiaDepartment of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi ArabiaWe 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.http://dx.doi.org/10.1155/2013/376829 |
| spellingShingle | Mohammed Alshahrani Qamrul Hasan Ansari Suliman Al-Homidan Existence Results for Nonsmooth Vector Quasi-Variational-Like Inequalities Abstract and Applied Analysis |
| title | Existence Results for Nonsmooth Vector Quasi-Variational-Like Inequalities |
| title_full | Existence Results for Nonsmooth Vector Quasi-Variational-Like Inequalities |
| title_fullStr | Existence Results for Nonsmooth Vector Quasi-Variational-Like Inequalities |
| title_full_unstemmed | Existence Results for Nonsmooth Vector Quasi-Variational-Like Inequalities |
| title_short | Existence Results for Nonsmooth Vector Quasi-Variational-Like Inequalities |
| title_sort | existence results for nonsmooth vector quasi variational like inequalities |
| url | http://dx.doi.org/10.1155/2013/376829 |
| work_keys_str_mv | AT mohammedalshahrani existenceresultsfornonsmoothvectorquasivariationallikeinequalities AT qamrulhasanansari existenceresultsfornonsmoothvectorquasivariationallikeinequalities AT sulimanalhomidan existenceresultsfornonsmoothvectorquasivariationallikeinequalities |