A Hybrid Proximal Algorithm for the Sum of Monotone Operators with Multivalued Mappings
We modify a hybrid method and a proximal point algorithm to iteratively find a zero point of the sum of two monotone operators and fixed point of nonspreading multivalued mappings in a Hilbert space by using the technique of forward-backward splitting method. The strong convergence theorem is establ...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/2409375 |
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| _version_ | 1849468055729471488 |
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| author | N. Kaewyong L. Kittiratanawasin C. Pukdeboon K. Sitthithakerngkiet |
| author_facet | N. Kaewyong L. Kittiratanawasin C. Pukdeboon K. Sitthithakerngkiet |
| author_sort | N. Kaewyong |
| collection | DOAJ |
| description | We modify a hybrid method and a proximal point algorithm to iteratively find a zero point of the sum of two monotone operators and fixed point of nonspreading multivalued mappings in a Hilbert space by using the technique of forward-backward splitting method. The strong convergence theorem is established and the illustrative numerical example is presented on this work. The results of this paper extend and improve some well-known results in the literature. |
| format | Article |
| id | doaj-art-fac3d5ce7ed74dcea4eca052479daf7a |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-fac3d5ce7ed74dcea4eca052479daf7a2025-08-20T03:25:57ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/24093752409375A Hybrid Proximal Algorithm for the Sum of Monotone Operators with Multivalued MappingsN. Kaewyong0L. Kittiratanawasin1C. Pukdeboon2K. Sitthithakerngkiet3Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), 1518, Pracharat 1 Road, Wongsawang, Bangsue, Bangkok 10800, ThailandDepartment of Mathematics, Faculty of Science, Kasetsart University, 50 Ngam Wong Wan Road, Ladyaow, Chatuchak, Bangkok 10900, ThailandNonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), 1518 Pracharat 1 Road, Wongsawang, Bangsue, Bangkok 10800, ThailandNonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), 1518 Pracharat 1 Road, Wongsawang, Bangsue, Bangkok 10800, ThailandWe modify a hybrid method and a proximal point algorithm to iteratively find a zero point of the sum of two monotone operators and fixed point of nonspreading multivalued mappings in a Hilbert space by using the technique of forward-backward splitting method. The strong convergence theorem is established and the illustrative numerical example is presented on this work. The results of this paper extend and improve some well-known results in the literature.http://dx.doi.org/10.1155/2018/2409375 |
| spellingShingle | N. Kaewyong L. Kittiratanawasin C. Pukdeboon K. Sitthithakerngkiet A Hybrid Proximal Algorithm for the Sum of Monotone Operators with Multivalued Mappings Journal of Function Spaces |
| title | A Hybrid Proximal Algorithm for the Sum of Monotone Operators with Multivalued Mappings |
| title_full | A Hybrid Proximal Algorithm for the Sum of Monotone Operators with Multivalued Mappings |
| title_fullStr | A Hybrid Proximal Algorithm for the Sum of Monotone Operators with Multivalued Mappings |
| title_full_unstemmed | A Hybrid Proximal Algorithm for the Sum of Monotone Operators with Multivalued Mappings |
| title_short | A Hybrid Proximal Algorithm for the Sum of Monotone Operators with Multivalued Mappings |
| title_sort | hybrid proximal algorithm for the sum of monotone operators with multivalued mappings |
| url | http://dx.doi.org/10.1155/2018/2409375 |
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