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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |