A new self-adaptive method for solving resolvent of sum of two monotone operators in Banach spaces
Abstract We introduce a Tseng extragradient method for solving monotone inclusion problem in Banach space. A strong convergence result of an Halpern inertial extrapolation method for solving the resolvent of sum of two monotone operators without the knowledge of the Lipschitz constant was establishe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-12-01
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| Series: | Fixed Point Theory and Algorithms for Sciences and Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13663-023-00753-y |
| _version_ | 1797388135860011008 |
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| author | H. A. Abass M. Aphane O. K. Oyewole |
| author_facet | H. A. Abass M. Aphane O. K. Oyewole |
| author_sort | H. A. Abass |
| collection | DOAJ |
| description | Abstract We introduce a Tseng extragradient method for solving monotone inclusion problem in Banach space. A strong convergence result of an Halpern inertial extrapolation method for solving the resolvent of sum of two monotone operators without the knowledge of the Lipschitz constant was established. Lastly, we illustrate some numerical behavior of our iterative scheme to showcase the performance of the proposed method compared to other related results in the literature. |
| first_indexed | 2024-03-08T22:36:28Z |
| format | Article |
| id | doaj.art-7571ccc68f83474a93e6e925c7e72d78 |
| institution | Directory Open Access Journal |
| issn | 2730-5422 |
| language | English |
| last_indexed | 2024-03-08T22:36:28Z |
| publishDate | 2023-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Algorithms for Sciences and Engineering |
| spelling | doaj.art-7571ccc68f83474a93e6e925c7e72d782023-12-17T12:27:35ZengSpringerOpenFixed Point Theory and Algorithms for Sciences and Engineering2730-54222023-12-012023111910.1186/s13663-023-00753-yA new self-adaptive method for solving resolvent of sum of two monotone operators in Banach spacesH. A. Abass0M. Aphane1O. K. Oyewole2Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences UniversityDepartment of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences UniversityDepartment of Mathematics, The Technion-Israel Institute of TechnologyAbstract We introduce a Tseng extragradient method for solving monotone inclusion problem in Banach space. A strong convergence result of an Halpern inertial extrapolation method for solving the resolvent of sum of two monotone operators without the knowledge of the Lipschitz constant was established. Lastly, we illustrate some numerical behavior of our iterative scheme to showcase the performance of the proposed method compared to other related results in the literature.https://doi.org/10.1186/s13663-023-00753-yMonotone inclusion problemBregman strongly nonexpansive mappingLipschitz continuousIterative method |
| spellingShingle | H. A. Abass M. Aphane O. K. Oyewole A new self-adaptive method for solving resolvent of sum of two monotone operators in Banach spaces Fixed Point Theory and Algorithms for Sciences and Engineering Monotone inclusion problem Bregman strongly nonexpansive mapping Lipschitz continuous Iterative method |
| title | A new self-adaptive method for solving resolvent of sum of two monotone operators in Banach spaces |
| title_full | A new self-adaptive method for solving resolvent of sum of two monotone operators in Banach spaces |
| title_fullStr | A new self-adaptive method for solving resolvent of sum of two monotone operators in Banach spaces |
| title_full_unstemmed | A new self-adaptive method for solving resolvent of sum of two monotone operators in Banach spaces |
| title_short | A new self-adaptive method for solving resolvent of sum of two monotone operators in Banach spaces |
| title_sort | new self adaptive method for solving resolvent of sum of two monotone operators in banach spaces |
| topic | Monotone inclusion problem Bregman strongly nonexpansive mapping Lipschitz continuous Iterative method |
| url | https://doi.org/10.1186/s13663-023-00753-y |
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