A Halpern-type algorithm for a common solution of nonlinear problems in Banach spaces
In this article, we propose a Halpern-type subgradient extragradient algorithm for solving a common element of the set of solutions of variational inequality problems for continuous monotone mappings and the set of f-fixed points of continuous f-pseudocontractive mappings in reflexive real Banach sp...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-03-01
|
| Series: | Topological Algebra and its Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/taa-2022-0133 |
| _version_ | 1797848588262309888 |
|---|---|
| author | Zegeye Habtu Boikanyo Oganeditse A. |
| author_facet | Zegeye Habtu Boikanyo Oganeditse A. |
| author_sort | Zegeye Habtu |
| collection | DOAJ |
| description | In this article, we propose a Halpern-type subgradient extragradient algorithm for solving a common element of the set of solutions of variational inequality problems for continuous monotone mappings and the set of f-fixed points of continuous f-pseudocontractive mappings in reflexive real Banach spaces. In addition, we prove a strong convergence theorem for the sequence generated by the algorithm. As a consequence, we obtain a scheme that converges strongly to a common f-fixed point of continuous f-pseudocontractive mappings and a scheme that converges strongly to a common zero of continuous monotone mappings in Banach spaces. Furthermore, we provide a numerical example to illustrate the implementability of our algorithm. |
| first_indexed | 2024-04-09T18:30:54Z |
| format | Article |
| id | doaj.art-743dde86dd9a49a08d3d5f4c7e803b91 |
| institution | Directory Open Access Journal |
| issn | 2299-3231 |
| language | English |
| last_indexed | 2024-04-09T18:30:54Z |
| publishDate | 2023-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Topological Algebra and its Applications |
| spelling | doaj.art-743dde86dd9a49a08d3d5f4c7e803b912023-04-11T17:07:20ZengDe GruyterTopological Algebra and its Applications2299-32312023-03-0111154557410.1515/taa-2022-0133A Halpern-type algorithm for a common solution of nonlinear problems in Banach spacesZegeye Habtu0Boikanyo Oganeditse A.1Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Private Bag 16, Palapye 276, BotswanaDepartment of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Private Bag 16, Palapye 276, BotswanaIn this article, we propose a Halpern-type subgradient extragradient algorithm for solving a common element of the set of solutions of variational inequality problems for continuous monotone mappings and the set of f-fixed points of continuous f-pseudocontractive mappings in reflexive real Banach spaces. In addition, we prove a strong convergence theorem for the sequence generated by the algorithm. As a consequence, we obtain a scheme that converges strongly to a common f-fixed point of continuous f-pseudocontractive mappings and a scheme that converges strongly to a common zero of continuous monotone mappings in Banach spaces. Furthermore, we provide a numerical example to illustrate the implementability of our algorithm.https://doi.org/10.1515/taa-2022-0133f-fixed pointf-pseudocontractive mappingmonotone mappingsemi-pseudocontractive mappingvariational inequalitystrong convergencezero points47h0547h1047j2547j0547j2047j26 |
| spellingShingle | Zegeye Habtu Boikanyo Oganeditse A. A Halpern-type algorithm for a common solution of nonlinear problems in Banach spaces Topological Algebra and its Applications f-fixed point f-pseudocontractive mapping monotone mapping semi-pseudocontractive mapping variational inequality strong convergence zero points 47h05 47h10 47j25 47j05 47j20 47j26 |
| title | A Halpern-type algorithm for a common solution of nonlinear problems in Banach spaces |
| title_full | A Halpern-type algorithm for a common solution of nonlinear problems in Banach spaces |
| title_fullStr | A Halpern-type algorithm for a common solution of nonlinear problems in Banach spaces |
| title_full_unstemmed | A Halpern-type algorithm for a common solution of nonlinear problems in Banach spaces |
| title_short | A Halpern-type algorithm for a common solution of nonlinear problems in Banach spaces |
| title_sort | halpern type algorithm for a common solution of nonlinear problems in banach spaces |
| topic | f-fixed point f-pseudocontractive mapping monotone mapping semi-pseudocontractive mapping variational inequality strong convergence zero points 47h05 47h10 47j25 47j05 47j20 47j26 |
| url | https://doi.org/10.1515/taa-2022-0133 |
| work_keys_str_mv | AT zegeyehabtu ahalperntypealgorithmforacommonsolutionofnonlinearproblemsinbanachspaces AT boikanyooganeditsea ahalperntypealgorithmforacommonsolutionofnonlinearproblemsinbanachspaces AT zegeyehabtu halperntypealgorithmforacommonsolutionofnonlinearproblemsinbanachspaces AT boikanyooganeditsea halperntypealgorithmforacommonsolutionofnonlinearproblemsinbanachspaces |