A self-adaptive Tseng extragradient method for solving monotone variational inequality and fixed point problems in Banach spaces
In this paper, we introduce a self-adaptive projection method for finding a common element in the solution set of variational inequalities (VIs) and fixed point set for relatively nonexpansive mappings in 2-uniformly convex and uniformly smooth real Banach spaces. We prove a strong convergence resul...
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| Format: | Article |
| Language: | English |
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De Gruyter
2021-12-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2021-0016 |
| _version_ | 1818488007348453376 |
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| author | Jolaoso Lateef Olakunle |
| author_facet | Jolaoso Lateef Olakunle |
| author_sort | Jolaoso Lateef Olakunle |
| collection | DOAJ |
| description | In this paper, we introduce a self-adaptive projection method for finding a common element in the solution set of variational inequalities (VIs) and fixed point set for relatively nonexpansive mappings in 2-uniformly convex and uniformly smooth real Banach spaces. We prove a strong convergence result for the sequence generated by our algorithm without imposing a Lipschitz condition on the cost operator of the VIs. We also provide some numerical examples to illustrate the performance of the proposed algorithm by comparing with related methods in the literature. This result extends and improves some recent results in the literature in this direction. |
| first_indexed | 2024-12-10T16:45:36Z |
| format | Article |
| id | doaj.art-be6d400a50bd4645b9b23d5fc81d5422 |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-12-10T16:45:36Z |
| publishDate | 2021-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-be6d400a50bd4645b9b23d5fc81d54222022-12-22T01:41:05ZengDe GruyterDemonstratio Mathematica2391-46612021-12-0154152754710.1515/dema-2021-0016A self-adaptive Tseng extragradient method for solving monotone variational inequality and fixed point problems in Banach spacesJolaoso Lateef Olakunle0Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94 Medunsa 0204, Pretoria, South AfricaIn this paper, we introduce a self-adaptive projection method for finding a common element in the solution set of variational inequalities (VIs) and fixed point set for relatively nonexpansive mappings in 2-uniformly convex and uniformly smooth real Banach spaces. We prove a strong convergence result for the sequence generated by our algorithm without imposing a Lipschitz condition on the cost operator of the VIs. We also provide some numerical examples to illustrate the performance of the proposed algorithm by comparing with related methods in the literature. This result extends and improves some recent results in the literature in this direction.https://doi.org/10.1515/dema-2021-0016variational inequalitymonotone operatorself-adaptiveprojection methodbanach spaces65k1547j2565j1590c33 |
| spellingShingle | Jolaoso Lateef Olakunle A self-adaptive Tseng extragradient method for solving monotone variational inequality and fixed point problems in Banach spaces Demonstratio Mathematica variational inequality monotone operator self-adaptive projection method banach spaces 65k15 47j25 65j15 90c33 |
| title | A self-adaptive Tseng extragradient method for solving monotone variational inequality and fixed point problems in Banach spaces |
| title_full | A self-adaptive Tseng extragradient method for solving monotone variational inequality and fixed point problems in Banach spaces |
| title_fullStr | A self-adaptive Tseng extragradient method for solving monotone variational inequality and fixed point problems in Banach spaces |
| title_full_unstemmed | A self-adaptive Tseng extragradient method for solving monotone variational inequality and fixed point problems in Banach spaces |
| title_short | A self-adaptive Tseng extragradient method for solving monotone variational inequality and fixed point problems in Banach spaces |
| title_sort | self adaptive tseng extragradient method for solving monotone variational inequality and fixed point problems in banach spaces |
| topic | variational inequality monotone operator self-adaptive projection method banach spaces 65k15 47j25 65j15 90c33 |
| url | https://doi.org/10.1515/dema-2021-0016 |
| work_keys_str_mv | AT jolaosolateefolakunle aselfadaptivetsengextragradientmethodforsolvingmonotonevariationalinequalityandfixedpointproblemsinbanachspaces AT jolaosolateefolakunle selfadaptivetsengextragradientmethodforsolvingmonotonevariationalinequalityandfixedpointproblemsinbanachspaces |