Inertial iterative method with self-adaptive step size for finite family of split monotone variational inclusion and fixed point problems in Banach spaces
In this paper, we propose and study a new inertial iterative algorithm with self-adaptive step size for approximating a common solution of finite family of split monotone variational inclusion problems and fixed point problem of a nonexpansive mapping between a Banach space and a Hilbert space. This...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-06-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2022-0005 |
| _version_ | 1828169919637749760 |
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| author | Ogwo Grace N. Alakoya Timilehin O. Mewomo Oluwatosin T. |
| author_facet | Ogwo Grace N. Alakoya Timilehin O. Mewomo Oluwatosin T. |
| author_sort | Ogwo Grace N. |
| collection | DOAJ |
| description | In this paper, we propose and study a new inertial iterative algorithm with self-adaptive step size for approximating a common solution of finite family of split monotone variational inclusion problems and fixed point problem of a nonexpansive mapping between a Banach space and a Hilbert space. This method combines the inertial technique with viscosity method and self-adaptive step size for solving the common solution problem. We prove a strong convergence result for the proposed method under some mild conditions. Moreover, we apply our result to study the split feasibility problem and split minimization problem. Finally, we provide some numerical experiments to demonstrate the efficiency of our method in comparison with some well-known methods in the literature. Our method does not require prior knowledge or estimate of the operator norm, which makes it easily implementable unlike so many other methods in the literature, which require prior knowledge of the operator norm for their implementation. |
| first_indexed | 2024-04-12T03:00:04Z |
| format | Article |
| id | doaj.art-e770453aa126447281f47f062897f1ba |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-04-12T03:00:04Z |
| publishDate | 2022-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-e770453aa126447281f47f062897f1ba2022-12-22T03:50:42ZengDe GruyterDemonstratio Mathematica2391-46612022-06-0155119321610.1515/dema-2022-0005Inertial iterative method with self-adaptive step size for finite family of split monotone variational inclusion and fixed point problems in Banach spacesOgwo Grace N.0Alakoya Timilehin O.1Mewomo Oluwatosin T.2School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South AfricaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South AfricaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South AfricaIn this paper, we propose and study a new inertial iterative algorithm with self-adaptive step size for approximating a common solution of finite family of split monotone variational inclusion problems and fixed point problem of a nonexpansive mapping between a Banach space and a Hilbert space. This method combines the inertial technique with viscosity method and self-adaptive step size for solving the common solution problem. We prove a strong convergence result for the proposed method under some mild conditions. Moreover, we apply our result to study the split feasibility problem and split minimization problem. Finally, we provide some numerical experiments to demonstrate the efficiency of our method in comparison with some well-known methods in the literature. Our method does not require prior knowledge or estimate of the operator norm, which makes it easily implementable unlike so many other methods in the literature, which require prior knowledge of the operator norm for their implementation.https://doi.org/10.1515/dema-2022-0005split monotone variational inclusion problemnonexpansive mappingslipschitzianfixed point problemiterative schemesplit feasibility problemsplit minimization problem47h0647h0946n10 |
| spellingShingle | Ogwo Grace N. Alakoya Timilehin O. Mewomo Oluwatosin T. Inertial iterative method with self-adaptive step size for finite family of split monotone variational inclusion and fixed point problems in Banach spaces Demonstratio Mathematica split monotone variational inclusion problem nonexpansive mappings lipschitzian fixed point problem iterative scheme split feasibility problem split minimization problem 47h06 47h09 46n10 |
| title | Inertial iterative method with self-adaptive step size for finite family of split monotone variational inclusion and fixed point problems in Banach spaces |
| title_full | Inertial iterative method with self-adaptive step size for finite family of split monotone variational inclusion and fixed point problems in Banach spaces |
| title_fullStr | Inertial iterative method with self-adaptive step size for finite family of split monotone variational inclusion and fixed point problems in Banach spaces |
| title_full_unstemmed | Inertial iterative method with self-adaptive step size for finite family of split monotone variational inclusion and fixed point problems in Banach spaces |
| title_short | Inertial iterative method with self-adaptive step size for finite family of split monotone variational inclusion and fixed point problems in Banach spaces |
| title_sort | inertial iterative method with self adaptive step size for finite family of split monotone variational inclusion and fixed point problems in banach spaces |
| topic | split monotone variational inclusion problem nonexpansive mappings lipschitzian fixed point problem iterative scheme split feasibility problem split minimization problem 47h06 47h09 46n10 |
| url | https://doi.org/10.1515/dema-2022-0005 |
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