Convergence analysis of a general inertial projection-type method for solving pseudomonotone equilibrium problems with applications
Abstract In this paper, we introduce a new algorithm by incorporating an inertial term with a subgradient extragradient algorithm to solve the equilibrium problems involving a pseudomonotone and Lipschitz-type continuous bifunction in real Hilbert spaces. A weak convergence theorem is well establish...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-04-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-021-02591-1 |
| _version_ | 1823966491176861696 |
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| author | Habib ur Rehman Poom Kumam Aviv Gibali Wiyada Kumam |
| author_facet | Habib ur Rehman Poom Kumam Aviv Gibali Wiyada Kumam |
| author_sort | Habib ur Rehman |
| collection | DOAJ |
| description | Abstract In this paper, we introduce a new algorithm by incorporating an inertial term with a subgradient extragradient algorithm to solve the equilibrium problems involving a pseudomonotone and Lipschitz-type continuous bifunction in real Hilbert spaces. A weak convergence theorem is well established under certain mild conditions for the bifunction and the control parameters involved. Some of the applications to solve variational inequalities and fixed point problems are considered. Finally, several numerical experiments are performed to demonstrate the numerical efficacy and superiority of the proposed algorithm over other well-known existing algorithms. |
| first_indexed | 2024-12-17T18:13:21Z |
| format | Article |
| id | doaj.art-5a7187ba0d7e4605a10f18366a1921b5 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-17T18:13:21Z |
| publishDate | 2021-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-5a7187ba0d7e4605a10f18366a1921b52022-12-21T21:37:48ZengSpringerOpenJournal of Inequalities and Applications1029-242X2021-04-012021112710.1186/s13660-021-02591-1Convergence analysis of a general inertial projection-type method for solving pseudomonotone equilibrium problems with applicationsHabib ur Rehman0Poom Kumam1Aviv Gibali2Wiyada Kumam3Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT)Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT)Department of Mathematics, ORT Braude CollegeProgram in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology ThanyaburiAbstract In this paper, we introduce a new algorithm by incorporating an inertial term with a subgradient extragradient algorithm to solve the equilibrium problems involving a pseudomonotone and Lipschitz-type continuous bifunction in real Hilbert spaces. A weak convergence theorem is well established under certain mild conditions for the bifunction and the control parameters involved. Some of the applications to solve variational inequalities and fixed point problems are considered. Finally, several numerical experiments are performed to demonstrate the numerical efficacy and superiority of the proposed algorithm over other well-known existing algorithms.https://doi.org/10.1186/s13660-021-02591-1Pseudomonotone bifunctionEquilibrium problemWeak convergenceLipschitz-type conditionsVariational inequality problem |
| spellingShingle | Habib ur Rehman Poom Kumam Aviv Gibali Wiyada Kumam Convergence analysis of a general inertial projection-type method for solving pseudomonotone equilibrium problems with applications Journal of Inequalities and Applications Pseudomonotone bifunction Equilibrium problem Weak convergence Lipschitz-type conditions Variational inequality problem |
| title | Convergence analysis of a general inertial projection-type method for solving pseudomonotone equilibrium problems with applications |
| title_full | Convergence analysis of a general inertial projection-type method for solving pseudomonotone equilibrium problems with applications |
| title_fullStr | Convergence analysis of a general inertial projection-type method for solving pseudomonotone equilibrium problems with applications |
| title_full_unstemmed | Convergence analysis of a general inertial projection-type method for solving pseudomonotone equilibrium problems with applications |
| title_short | Convergence analysis of a general inertial projection-type method for solving pseudomonotone equilibrium problems with applications |
| title_sort | convergence analysis of a general inertial projection type method for solving pseudomonotone equilibrium problems with applications |
| topic | Pseudomonotone bifunction Equilibrium problem Weak convergence Lipschitz-type conditions Variational inequality problem |
| url | https://doi.org/10.1186/s13660-021-02591-1 |
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