Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its Applications
In this article, we discuss the hierarchical fixed point and split monotone variational inclusion problems and propose a new iterative method with the inertial terms involving a step size to avoid the difficulty of calculating the operator norm in real Hilbert spaces. A strong convergence theorem of...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/19/2460 |
| _version_ | 1797516027899150336 |
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| author | Preeyanuch Chuasuk Anchalee Kaewcharoen |
| author_facet | Preeyanuch Chuasuk Anchalee Kaewcharoen |
| author_sort | Preeyanuch Chuasuk |
| collection | DOAJ |
| description | In this article, we discuss the hierarchical fixed point and split monotone variational inclusion problems and propose a new iterative method with the inertial terms involving a step size to avoid the difficulty of calculating the operator norm in real Hilbert spaces. A strong convergence theorem of the proposed method is established under some suitable control conditions. Furthermore, the proposed method is modified and used to derive a scheme for solving the split problems. Finally, we compare and demonstrate the efficiency and applicability of our schemes for numerical experiments as well as an example in the field of image restoration. |
| first_indexed | 2024-03-10T06:55:33Z |
| format | Article |
| id | doaj.art-f0ecf29aa19f4604afedbc877615b924 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T06:55:33Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f0ecf29aa19f4604afedbc877615b9242023-11-22T16:30:40ZengMDPI AGMathematics2227-73902021-10-01919246010.3390/math9192460Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its ApplicationsPreeyanuch Chuasuk0Anchalee Kaewcharoen1Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, ThailandDepartment of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandIn this article, we discuss the hierarchical fixed point and split monotone variational inclusion problems and propose a new iterative method with the inertial terms involving a step size to avoid the difficulty of calculating the operator norm in real Hilbert spaces. A strong convergence theorem of the proposed method is established under some suitable control conditions. Furthermore, the proposed method is modified and used to derive a scheme for solving the split problems. Finally, we compare and demonstrate the efficiency and applicability of our schemes for numerical experiments as well as an example in the field of image restoration.https://www.mdpi.com/2227-7390/9/19/2460variational inclusion probleminertial techniquestrong convergenceimage restorationhierarchical fixed point problem |
| spellingShingle | Preeyanuch Chuasuk Anchalee Kaewcharoen Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its Applications Mathematics variational inclusion problem inertial technique strong convergence image restoration hierarchical fixed point problem |
| title | Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its Applications |
| title_full | Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its Applications |
| title_fullStr | Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its Applications |
| title_full_unstemmed | Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its Applications |
| title_short | Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its Applications |
| title_sort | inertial krasnoselski mann iterative method for solving hierarchical fixed point and split monotone variational inclusion problems with its applications |
| topic | variational inclusion problem inertial technique strong convergence image restoration hierarchical fixed point problem |
| url | https://www.mdpi.com/2227-7390/9/19/2460 |
| work_keys_str_mv | AT preeyanuchchuasuk inertialkrasnoselskimanniterativemethodforsolvinghierarchicalfixedpointandsplitmonotonevariationalinclusionproblemswithitsapplications AT anchaleekaewcharoen inertialkrasnoselskimanniterativemethodforsolvinghierarchicalfixedpointandsplitmonotonevariationalinclusionproblemswithitsapplications |