An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces
In this paper, we propose an iterative scheme for a special split feasibility problem with the maximal monotone operator and fixed-point problem in Banach spaces. The algorithm implements Halpern’s iteration with an inertial technique for the problem. Under some mild assumption of the monotonicity o...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9974351 |
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| author | Huijuan Jia Shufen Liu Yazheng Dang |
| author_facet | Huijuan Jia Shufen Liu Yazheng Dang |
| author_sort | Huijuan Jia |
| collection | DOAJ |
| description | In this paper, we propose an iterative scheme for a special split feasibility problem with the maximal monotone operator and fixed-point problem in Banach spaces. The algorithm implements Halpern’s iteration with an inertial technique for the problem. Under some mild assumption of the monotonicity of the related mapping, we establish the strong convergence of the sequence generated by the algorithm which does not require the spectral radius of ATA. Finally, the numerical example is presented to demonstrate the efficiency of the algorithm. |
| format | Article |
| id | doaj-art-2a3bf9af3aef42a185b0ee2f24477bc3 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-2a3bf9af3aef42a185b0ee2f24477bc32025-02-03T06:46:14ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/99743519974351An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach SpacesHuijuan Jia0Shufen Liu1Yazheng Dang2College of Computer Science and Technology, Jilin University, 2699 Qianjin Street, Chaoyang District, Changchun 130012, ChinaCollege of Computer Science and Technology, Jilin University, 2699 Qianjin Street, Chaoyang District, Changchun 130012, ChinaSchool of Business, University of Shanghai for Science and Technology, 516 Jungong Road, Yangpu District, Shanghai 200093, ChinaIn this paper, we propose an iterative scheme for a special split feasibility problem with the maximal monotone operator and fixed-point problem in Banach spaces. The algorithm implements Halpern’s iteration with an inertial technique for the problem. Under some mild assumption of the monotonicity of the related mapping, we establish the strong convergence of the sequence generated by the algorithm which does not require the spectral radius of ATA. Finally, the numerical example is presented to demonstrate the efficiency of the algorithm.http://dx.doi.org/10.1155/2021/9974351 |
| spellingShingle | Huijuan Jia Shufen Liu Yazheng Dang An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces Journal of Mathematics |
| title | An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces |
| title_full | An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces |
| title_fullStr | An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces |
| title_full_unstemmed | An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces |
| title_short | An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces |
| title_sort | inertial iterative algorithm with strong convergence for solving modified split feasibility problem in banach spaces |
| url | http://dx.doi.org/10.1155/2021/9974351 |
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