Strong Convergence of an Inertial Iterative Algorithm for Generalized Mixed Variational-like Inequality Problem and Bregman Relatively Nonexpansive Mapping in Reflexive Banach Space
In this paper, we consider a generalized mixed variational-like inequality problem and prove a Minty-type lemma for its related auxiliary problems in a real Banach space. We prove the existence of a solution of these auxiliary problems and also prove some properties for the solution set of generaliz...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9421449 |
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| _version_ | 1832547274495885312 |
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| author | Saud Fahad Aldosary Watcharaporn Cholamjiak Rehan Ali Mohammad Farid |
| author_facet | Saud Fahad Aldosary Watcharaporn Cholamjiak Rehan Ali Mohammad Farid |
| author_sort | Saud Fahad Aldosary |
| collection | DOAJ |
| description | In this paper, we consider a generalized mixed variational-like inequality problem and prove a Minty-type lemma for its related auxiliary problems in a real Banach space. We prove the existence of a solution of these auxiliary problems and also prove some properties for the solution set of generalized mixed variational-like inequality problem. Furthermore, we introduce and study an inertial hybrid iterative method for solving the generalized mixed variational-like inequality problem involving Bregman relatively nonexpansive mapping in Banach space. We study the strong convergence for the proposed algorithm. Finally, we list some consequences and computational examples to emphasize the efficiency and relevancy of the main result. |
| format | Article |
| id | doaj-art-275c53e5487a425282d3a33da97c8672 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-275c53e5487a425282d3a33da97c86722025-02-03T06:45:20ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/9421449Strong Convergence of an Inertial Iterative Algorithm for Generalized Mixed Variational-like Inequality Problem and Bregman Relatively Nonexpansive Mapping in Reflexive Banach SpaceSaud Fahad Aldosary0Watcharaporn Cholamjiak1Rehan Ali2Mohammad Farid3Department of MathematicsSchool of ScienceDepartment of MathematicsDepartment of MathematicsIn this paper, we consider a generalized mixed variational-like inequality problem and prove a Minty-type lemma for its related auxiliary problems in a real Banach space. We prove the existence of a solution of these auxiliary problems and also prove some properties for the solution set of generalized mixed variational-like inequality problem. Furthermore, we introduce and study an inertial hybrid iterative method for solving the generalized mixed variational-like inequality problem involving Bregman relatively nonexpansive mapping in Banach space. We study the strong convergence for the proposed algorithm. Finally, we list some consequences and computational examples to emphasize the efficiency and relevancy of the main result.http://dx.doi.org/10.1155/2021/9421449 |
| spellingShingle | Saud Fahad Aldosary Watcharaporn Cholamjiak Rehan Ali Mohammad Farid Strong Convergence of an Inertial Iterative Algorithm for Generalized Mixed Variational-like Inequality Problem and Bregman Relatively Nonexpansive Mapping in Reflexive Banach Space Journal of Mathematics |
| title | Strong Convergence of an Inertial Iterative Algorithm for Generalized Mixed Variational-like Inequality Problem and Bregman Relatively Nonexpansive Mapping in Reflexive Banach Space |
| title_full | Strong Convergence of an Inertial Iterative Algorithm for Generalized Mixed Variational-like Inequality Problem and Bregman Relatively Nonexpansive Mapping in Reflexive Banach Space |
| title_fullStr | Strong Convergence of an Inertial Iterative Algorithm for Generalized Mixed Variational-like Inequality Problem and Bregman Relatively Nonexpansive Mapping in Reflexive Banach Space |
| title_full_unstemmed | Strong Convergence of an Inertial Iterative Algorithm for Generalized Mixed Variational-like Inequality Problem and Bregman Relatively Nonexpansive Mapping in Reflexive Banach Space |
| title_short | Strong Convergence of an Inertial Iterative Algorithm for Generalized Mixed Variational-like Inequality Problem and Bregman Relatively Nonexpansive Mapping in Reflexive Banach Space |
| title_sort | strong convergence of an inertial iterative algorithm for generalized mixed variational like inequality problem and bregman relatively nonexpansive mapping in reflexive banach space |
| url | http://dx.doi.org/10.1155/2021/9421449 |
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