A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications
A new system of generalized mixed quasivariational inclusions (for short, SGMQVI) with relaxed cocoercive operators, which develop some preexisting variational inequalities, is introduced and investigated in Banach spaces. Next, the existence and uniqueness of solutions to the problem (SGMQVI) are e...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/961038 |
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| author | Zhongping Wan Jia-Wei Chen Hai Sun Liuyang Yuan |
| author_facet | Zhongping Wan Jia-Wei Chen Hai Sun Liuyang Yuan |
| author_sort | Zhongping Wan |
| collection | DOAJ |
| description | A new system of generalized mixed quasivariational inclusions
(for short, SGMQVI) with relaxed cocoercive operators, which develop some preexisting
variational inequalities, is introduced and investigated in Banach spaces. Next, the existence and uniqueness of solutions to the problem (SGMQVI) are established in real Banach
spaces. From fixed point perspective, we propose some new iterative algorithms for solving
the system of generalized mixed quasivariational inclusion problem (SGMQVI). Moreover,
strong convergence theorems of these iterative sequences generated by the corresponding
algorithms are proved under suitable conditions. As an application, the strong convergence
theorem for a class of bilevel variational inequalities is derived in Hilbert space. The main
results in this paper develop, improve, and unify some well-known results in the literature. |
| format | Article |
| id | doaj-art-97bd99f78f2243fdaed631c604cc1971 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-97bd99f78f2243fdaed631c604cc19712025-02-03T01:33:10ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/961038961038A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and ApplicationsZhongping Wan0Jia-Wei Chen1Hai Sun2Liuyang Yuan3School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, ChinaSchool of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, ChinaSchool of Mathematics and Information, China West Normal University, Nanchong, Sichuan 637002, ChinaSchool of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, ChinaA new system of generalized mixed quasivariational inclusions (for short, SGMQVI) with relaxed cocoercive operators, which develop some preexisting variational inequalities, is introduced and investigated in Banach spaces. Next, the existence and uniqueness of solutions to the problem (SGMQVI) are established in real Banach spaces. From fixed point perspective, we propose some new iterative algorithms for solving the system of generalized mixed quasivariational inclusion problem (SGMQVI). Moreover, strong convergence theorems of these iterative sequences generated by the corresponding algorithms are proved under suitable conditions. As an application, the strong convergence theorem for a class of bilevel variational inequalities is derived in Hilbert space. The main results in this paper develop, improve, and unify some well-known results in the literature.http://dx.doi.org/10.1155/2011/961038 |
| spellingShingle | Zhongping Wan Jia-Wei Chen Hai Sun Liuyang Yuan A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications Journal of Applied Mathematics |
| title | A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications |
| title_full | A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications |
| title_fullStr | A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications |
| title_full_unstemmed | A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications |
| title_short | A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications |
| title_sort | new system of generalized mixed quasivariational inclusions with relaxed cocoercive operators and applications |
| url | http://dx.doi.org/10.1155/2011/961038 |
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