H(⋅,⋅)-Cocoercive Operator and an Application for Solving Generalized Variational Inclusions
The purpose of this paper is to introduce a new H(⋅,⋅)-cocoercive operator, which generalizes many existing monotone operators. The resolvent operator associated with H(⋅,⋅)-cocoercive operator is defined, and its Lipschitz continuity is presented. By using techniques of resolvent operator, a new it...
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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: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/261534 |
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| _version_ | 1832563451807924224 |
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| author | Rais Ahmad Mohd Dilshad Mu-Ming Wong Jen-Chin Yao |
| author_facet | Rais Ahmad Mohd Dilshad Mu-Ming Wong Jen-Chin Yao |
| author_sort | Rais Ahmad |
| collection | DOAJ |
| description | The purpose of this paper is to introduce a new H(⋅,⋅)-cocoercive operator, which generalizes many existing monotone operators. The resolvent operator associated
with H(⋅,⋅)-cocoercive operator is defined, and its Lipschitz continuity is presented. By using techniques of resolvent operator, a new iterative algorithm for solving generalized variational inclusions is constructed. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. For illustration, some examples are given. |
| format | Article |
| id | doaj-art-be8ee5845ac9466c82e75bbfc3193736 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-be8ee5845ac9466c82e75bbfc31937362025-02-03T01:20:15ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/261534261534H(⋅,⋅)-Cocoercive Operator and an Application for Solving Generalized Variational InclusionsRais Ahmad0Mohd Dilshad1Mu-Ming Wong2Jen-Chin Yao3Department of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Applied Mathematics, Chung Yuan Christian University, Chung Li 32023, TaiwanCenter for General Education, Kaohsiung Medical University, Kaohsiung 807, TaiwanThe purpose of this paper is to introduce a new H(⋅,⋅)-cocoercive operator, which generalizes many existing monotone operators. The resolvent operator associated with H(⋅,⋅)-cocoercive operator is defined, and its Lipschitz continuity is presented. By using techniques of resolvent operator, a new iterative algorithm for solving generalized variational inclusions is constructed. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. For illustration, some examples are given.http://dx.doi.org/10.1155/2011/261534 |
| spellingShingle | Rais Ahmad Mohd Dilshad Mu-Ming Wong Jen-Chin Yao H(⋅,⋅)-Cocoercive Operator and an Application for Solving Generalized Variational Inclusions Abstract and Applied Analysis |
| title | H(⋅,⋅)-Cocoercive Operator and an Application for Solving Generalized Variational Inclusions |
| title_full | H(⋅,⋅)-Cocoercive Operator and an Application for Solving Generalized Variational Inclusions |
| title_fullStr | H(⋅,⋅)-Cocoercive Operator and an Application for Solving Generalized Variational Inclusions |
| title_full_unstemmed | H(⋅,⋅)-Cocoercive Operator and an Application for Solving Generalized Variational Inclusions |
| title_short | H(⋅,⋅)-Cocoercive Operator and an Application for Solving Generalized Variational Inclusions |
| title_sort | h ⋅ ⋅ cocoercive operator and an application for solving generalized variational inclusions |
| url | http://dx.doi.org/10.1155/2011/261534 |
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