Convergence Analysis of New Construction Explicit Methods for Solving Equilibrium Programming and Fixed Point Problems
In this paper, we present improved iterative methods for evaluating the numerical solution of an equilibrium problem in a Hilbert space with a pseudomonotone and a Lipschitz-type bifunction. The method is built around two computing phases of a proximal-like mapping with inertial terms. Many such sim...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/1934975 |
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| _version_ | 1832554967827742720 |
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| author | Chainarong Khunpanuk Nuttapol Pakkaranang Bancha Panyanak |
| author_facet | Chainarong Khunpanuk Nuttapol Pakkaranang Bancha Panyanak |
| author_sort | Chainarong Khunpanuk |
| collection | DOAJ |
| description | In this paper, we present improved iterative methods for evaluating the numerical solution of an equilibrium problem in a Hilbert space with a pseudomonotone and a Lipschitz-type bifunction. The method is built around two computing phases of a proximal-like mapping with inertial terms. Many such simpler step size rules that do not involve line search are examined, allowing the technique to be enforced more effectively without knowledge of the Lipschitz-type constant of the cost bifunction. When the control parameter conditions are properly defined, the iterative sequences converge weakly on a particular solution to the problem. We provide weak convergence theorems without knowing the Lipschitz-type bifunction constants. A few numerical tests were performed, and the results demonstrated the appropriateness and rapid convergence of the new methods over traditional ones. |
| format | Article |
| id | doaj-art-8d47b1a4a6f446b5bf796121c60780ad |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-8d47b1a4a6f446b5bf796121c60780ad2025-02-03T05:49:57ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/1934975Convergence Analysis of New Construction Explicit Methods for Solving Equilibrium Programming and Fixed Point ProblemsChainarong Khunpanuk0Nuttapol Pakkaranang1Bancha Panyanak2Mathematics and Computing Science ProgramMathematics and Computing Science ProgramResearch Group in Mathematics and Applied MathematicsIn this paper, we present improved iterative methods for evaluating the numerical solution of an equilibrium problem in a Hilbert space with a pseudomonotone and a Lipschitz-type bifunction. The method is built around two computing phases of a proximal-like mapping with inertial terms. Many such simpler step size rules that do not involve line search are examined, allowing the technique to be enforced more effectively without knowledge of the Lipschitz-type constant of the cost bifunction. When the control parameter conditions are properly defined, the iterative sequences converge weakly on a particular solution to the problem. We provide weak convergence theorems without knowing the Lipschitz-type bifunction constants. A few numerical tests were performed, and the results demonstrated the appropriateness and rapid convergence of the new methods over traditional ones.http://dx.doi.org/10.1155/2022/1934975 |
| spellingShingle | Chainarong Khunpanuk Nuttapol Pakkaranang Bancha Panyanak Convergence Analysis of New Construction Explicit Methods for Solving Equilibrium Programming and Fixed Point Problems Journal of Function Spaces |
| title | Convergence Analysis of New Construction Explicit Methods for Solving Equilibrium Programming and Fixed Point Problems |
| title_full | Convergence Analysis of New Construction Explicit Methods for Solving Equilibrium Programming and Fixed Point Problems |
| title_fullStr | Convergence Analysis of New Construction Explicit Methods for Solving Equilibrium Programming and Fixed Point Problems |
| title_full_unstemmed | Convergence Analysis of New Construction Explicit Methods for Solving Equilibrium Programming and Fixed Point Problems |
| title_short | Convergence Analysis of New Construction Explicit Methods for Solving Equilibrium Programming and Fixed Point Problems |
| title_sort | convergence analysis of new construction explicit methods for solving equilibrium programming and fixed point problems |
| url | http://dx.doi.org/10.1155/2022/1934975 |
| work_keys_str_mv | AT chainarongkhunpanuk convergenceanalysisofnewconstructionexplicitmethodsforsolvingequilibriumprogrammingandfixedpointproblems AT nuttapolpakkaranang convergenceanalysisofnewconstructionexplicitmethodsforsolvingequilibriumprogrammingandfixedpointproblems AT banchapanyanak convergenceanalysisofnewconstructionexplicitmethodsforsolvingequilibriumprogrammingandfixedpointproblems |