Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications
The aim of this paper is to propose two new modified extragradient methods to solve the pseudo-monotone equilibrium problem in a real Hilbert space with the Lipschitz-type condition. The iterative schemes use a new step size rule that is updated on each iteration based on the value of previous itera...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2021-08-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2021-0030 |
| _version_ | 1818487984922558464 |
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| author | Pakkaranang Nuttapol Rehman Habib ur Kumam Wiyada |
| author_facet | Pakkaranang Nuttapol Rehman Habib ur Kumam Wiyada |
| author_sort | Pakkaranang Nuttapol |
| collection | DOAJ |
| description | The aim of this paper is to propose two new modified extragradient methods to solve the pseudo-monotone equilibrium problem in a real Hilbert space with the Lipschitz-type condition. The iterative schemes use a new step size rule that is updated on each iteration based on the value of previous iterations. By using mild conditions on a bi-function, two strong convergence theorems are established. The applications of proposed results are studied to solve variational inequalities and fixed point problems in the setting of real Hilbert spaces. Many numerical experiments have been provided in order to show the algorithmic performance of the proposed methods and compare them with the existing ones. |
| first_indexed | 2024-12-10T16:45:18Z |
| format | Article |
| id | doaj.art-7e43da8bd1de4736a2b0a6795810ce7f |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-12-10T16:45:18Z |
| publishDate | 2021-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-7e43da8bd1de4736a2b0a6795810ce7f2022-12-22T01:41:05ZengDe GruyterDemonstratio Mathematica2391-46612021-08-0154128029810.1515/dema-2021-0030Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applicationsPakkaranang Nuttapol0Rehman Habib ur1Kumam Wiyada2Department of Mathematics, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, ThailandDepartment of Mathematics, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, ThailandProgram in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Thanyaburi, Pathumthani 12110, ThailandThe aim of this paper is to propose two new modified extragradient methods to solve the pseudo-monotone equilibrium problem in a real Hilbert space with the Lipschitz-type condition. The iterative schemes use a new step size rule that is updated on each iteration based on the value of previous iterations. By using mild conditions on a bi-function, two strong convergence theorems are established. The applications of proposed results are studied to solve variational inequalities and fixed point problems in the setting of real Hilbert spaces. Many numerical experiments have been provided in order to show the algorithmic performance of the proposed methods and compare them with the existing ones.https://doi.org/10.1515/dema-2021-0030equilibrium problempseudomonotone bifunctionlipschitz-type conditionsstrong convergencevariational inequality problemsfixed point problem47j2547h0947h0647j05 |
| spellingShingle | Pakkaranang Nuttapol Rehman Habib ur Kumam Wiyada Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications Demonstratio Mathematica equilibrium problem pseudomonotone bifunction lipschitz-type conditions strong convergence variational inequality problems fixed point problem 47j25 47h09 47h06 47j05 |
| title | Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications |
| title_full | Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications |
| title_fullStr | Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications |
| title_full_unstemmed | Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications |
| title_short | Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications |
| title_sort | two strongly convergent self adaptive iterative schemes for solving pseudo monotone equilibrium problems with applications |
| topic | equilibrium problem pseudomonotone bifunction lipschitz-type conditions strong convergence variational inequality problems fixed point problem 47j25 47h09 47h06 47j05 |
| url | https://doi.org/10.1515/dema-2021-0030 |
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