Two step inertial Tseng method for solving monotone variational inclusion problem
In this paper, we examine the monotone variational inclusion problem with a maximal monotone operator and a Lipschitz continuous monotone operator. We propose two different iterative algorithms for solving the monotone variational inclusion problem, utilizing a new self-adaptive step size and a two-...
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| Language: | English |
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Elsevier
2025-02-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037425000093 |
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| author | Lehlogonolo Mokaba Hammed Anuoluwapo Abass Abubakar Adamu |
| author_facet | Lehlogonolo Mokaba Hammed Anuoluwapo Abass Abubakar Adamu |
| author_sort | Lehlogonolo Mokaba |
| collection | DOAJ |
| description | In this paper, we examine the monotone variational inclusion problem with a maximal monotone operator and a Lipschitz continuous monotone operator. We propose two different iterative algorithms for solving the monotone variational inclusion problem, utilizing a new self-adaptive step size and a two-step inertial technique. Under the assumption that the solution set of the monotone variational inclusion problem is nonempty, we prove weak and strong convergence theorems concerning the sequences generated by our proposed algorithms. The convergence is guaranteed under some mild assumptions. Some numerical experiments are presented to demonstrate the performance of our iterative algorithms in comparison with recent results in the literature. |
| format | Article |
| id | doaj-art-5309c4e3f4434d98b7df0a36131e8ae1 |
| institution | OA Journals |
| issn | 2590-0374 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj-art-5309c4e3f4434d98b7df0a36131e8ae12025-08-20T01:58:27ZengElsevierResults in Applied Mathematics2590-03742025-02-012510054510.1016/j.rinam.2025.100545Two step inertial Tseng method for solving monotone variational inclusion problemLehlogonolo Mokaba0Hammed Anuoluwapo Abass1Abubakar Adamu2Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Science University, P.O. Box 94, Pretoria 0204, South AfricaDepartment of Mathematics and Applied Mathematics, Sefako Makgatho Health Science University, P.O. Box 94, Pretoria 0204, South AfricaOperational research center in Healthcare, Near East University, TRNC Mersin 10, Nicosia 99138, Turkey; Charles Chidume Mathematics Institute, African University of Science and Technology, Abuja 900107, Nigeria; School of Mathematics, Chongqing Normal University, Chongqing 400047, China; Corresponding author at: Operational research center in Healthcare, Near East University, TRNC Mersin 10, Nicosia 99138, Turkey.In this paper, we examine the monotone variational inclusion problem with a maximal monotone operator and a Lipschitz continuous monotone operator. We propose two different iterative algorithms for solving the monotone variational inclusion problem, utilizing a new self-adaptive step size and a two-step inertial technique. Under the assumption that the solution set of the monotone variational inclusion problem is nonempty, we prove weak and strong convergence theorems concerning the sequences generated by our proposed algorithms. The convergence is guaranteed under some mild assumptions. Some numerical experiments are presented to demonstrate the performance of our iterative algorithms in comparison with recent results in the literature.http://www.sciencedirect.com/science/article/pii/S2590037425000093Inertial methodMonotone operatorTseng methodVariational inclusion |
| spellingShingle | Lehlogonolo Mokaba Hammed Anuoluwapo Abass Abubakar Adamu Two step inertial Tseng method for solving monotone variational inclusion problem Results in Applied Mathematics Inertial method Monotone operator Tseng method Variational inclusion |
| title | Two step inertial Tseng method for solving monotone variational inclusion problem |
| title_full | Two step inertial Tseng method for solving monotone variational inclusion problem |
| title_fullStr | Two step inertial Tseng method for solving monotone variational inclusion problem |
| title_full_unstemmed | Two step inertial Tseng method for solving monotone variational inclusion problem |
| title_short | Two step inertial Tseng method for solving monotone variational inclusion problem |
| title_sort | two step inertial tseng method for solving monotone variational inclusion problem |
| topic | Inertial method Monotone operator Tseng method Variational inclusion |
| url | http://www.sciencedirect.com/science/article/pii/S2590037425000093 |
| work_keys_str_mv | AT lehlogonolomokaba twostepinertialtsengmethodforsolvingmonotonevariationalinclusionproblem AT hammedanuoluwapoabass twostepinertialtsengmethodforsolvingmonotonevariationalinclusionproblem AT abubakaradamu twostepinertialtsengmethodforsolvingmonotonevariationalinclusionproblem |