A Generalized Viscosity Inertial Projection and Contraction Method for Pseudomonotone Variational Inequality and Fixed Point Problems
We introduce a new projection and contraction method with inertial and self-adaptive techniques for solving variational inequalities and split common fixed point problems in real Hilbert spaces. The stepsize of the algorithm is selected via a self-adaptive method and does not require prior estimate...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/11/2039 |
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| author | Lateef Olakunle Jolaoso Maggie Aphane |
| author_facet | Lateef Olakunle Jolaoso Maggie Aphane |
| author_sort | Lateef Olakunle Jolaoso |
| collection | DOAJ |
| description | We introduce a new projection and contraction method with inertial and self-adaptive techniques for solving variational inequalities and split common fixed point problems in real Hilbert spaces. The stepsize of the algorithm is selected via a self-adaptive method and does not require prior estimate of norm of the bounded linear operator. More so, the cost operator of the variational inequalities does not necessarily needs to satisfies Lipschitz condition. We prove a strong convergence result under some mild conditions and provide an application of our result to split common null point problems. Some numerical experiments are reported to illustrate the performance of the algorithm and compare with some existing methods. |
| first_indexed | 2024-03-10T14:50:14Z |
| format | Article |
| id | doaj.art-e81126b83a504697b1c2401219726ca9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:50:14Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e81126b83a504697b1c2401219726ca92023-11-20T21:05:20ZengMDPI AGMathematics2227-73902020-11-01811203910.3390/math8112039A Generalized Viscosity Inertial Projection and Contraction Method for Pseudomonotone Variational Inequality and Fixed Point ProblemsLateef Olakunle Jolaoso0Maggie Aphane1Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Pretoria 0204, South AfricaDepartment of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Pretoria 0204, South AfricaWe introduce a new projection and contraction method with inertial and self-adaptive techniques for solving variational inequalities and split common fixed point problems in real Hilbert spaces. The stepsize of the algorithm is selected via a self-adaptive method and does not require prior estimate of norm of the bounded linear operator. More so, the cost operator of the variational inequalities does not necessarily needs to satisfies Lipschitz condition. We prove a strong convergence result under some mild conditions and provide an application of our result to split common null point problems. Some numerical experiments are reported to illustrate the performance of the algorithm and compare with some existing methods.https://www.mdpi.com/2227-7390/8/11/2039variational inequalitiespseudomonotoneself adaptive stepsizeextragradient methodfixed pointstrong convergence |
| spellingShingle | Lateef Olakunle Jolaoso Maggie Aphane A Generalized Viscosity Inertial Projection and Contraction Method for Pseudomonotone Variational Inequality and Fixed Point Problems Mathematics variational inequalities pseudomonotone self adaptive stepsize extragradient method fixed point strong convergence |
| title | A Generalized Viscosity Inertial Projection and Contraction Method for Pseudomonotone Variational Inequality and Fixed Point Problems |
| title_full | A Generalized Viscosity Inertial Projection and Contraction Method for Pseudomonotone Variational Inequality and Fixed Point Problems |
| title_fullStr | A Generalized Viscosity Inertial Projection and Contraction Method for Pseudomonotone Variational Inequality and Fixed Point Problems |
| title_full_unstemmed | A Generalized Viscosity Inertial Projection and Contraction Method for Pseudomonotone Variational Inequality and Fixed Point Problems |
| title_short | A Generalized Viscosity Inertial Projection and Contraction Method for Pseudomonotone Variational Inequality and Fixed Point Problems |
| title_sort | generalized viscosity inertial projection and contraction method for pseudomonotone variational inequality and fixed point problems |
| topic | variational inequalities pseudomonotone self adaptive stepsize extragradient method fixed point strong convergence |
| url | https://www.mdpi.com/2227-7390/8/11/2039 |
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