A New Algorithm for the Common Solutions of a Generalized Variational Inequality System and a Nonlinear Operator Equation in Banach Spaces
We study a new algorithm for the common solutions of a generalized variational inequality system and the fixed points of an asymptotically non-expansive mapping in Banach spaces. Under some specific assumptions imposed on the control parameters, some strong convergence theorems for the sequence gene...
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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/2227-7390/8/11/1944 |
| _version_ | 1797548899484827648 |
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| author | Yuanheng Wang Cancan Li Lirong Lu |
| author_facet | Yuanheng Wang Cancan Li Lirong Lu |
| author_sort | Yuanheng Wang |
| collection | DOAJ |
| description | We study a new algorithm for the common solutions of a generalized variational inequality system and the fixed points of an asymptotically non-expansive mapping in Banach spaces. Under some specific assumptions imposed on the control parameters, some strong convergence theorems for the sequence generated by our new viscosity iterative scheme to approximate their common solutions are proved. As an application of our main results, we solve the standard constrained convex optimization problem. The results here generalize and improve some other authors’ recently corresponding results. |
| first_indexed | 2024-03-10T15:07:20Z |
| format | Article |
| id | doaj.art-b540d46eae3e4b4a9474cda74a0781b9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:07:20Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b540d46eae3e4b4a9474cda74a0781b92023-11-20T19:42:20ZengMDPI AGMathematics2227-73902020-11-01811194410.3390/math8111944A New Algorithm for the Common Solutions of a Generalized Variational Inequality System and a Nonlinear Operator Equation in Banach SpacesYuanheng Wang0Cancan Li1Lirong Lu2College of Mathematics and Computer Science, with College of Xingzhi, Zhejiang Normal University, 268 Yingbin Road, Jinhua 321004, Zhejiang, ChinaCollege of Mathematics and Computer Science, with College of Xingzhi, Zhejiang Normal University, 268 Yingbin Road, Jinhua 321004, Zhejiang, ChinaCollege of Mathematics and Computer Science, with College of Xingzhi, Zhejiang Normal University, 268 Yingbin Road, Jinhua 321004, Zhejiang, ChinaWe study a new algorithm for the common solutions of a generalized variational inequality system and the fixed points of an asymptotically non-expansive mapping in Banach spaces. Under some specific assumptions imposed on the control parameters, some strong convergence theorems for the sequence generated by our new viscosity iterative scheme to approximate their common solutions are proved. As an application of our main results, we solve the standard constrained convex optimization problem. The results here generalize and improve some other authors’ recently corresponding results.https://www.mdpi.com/2227-7390/8/11/1944asymptotically non-expansive mappinggeneral variational inequality systemstrong convergenceBanach space |
| spellingShingle | Yuanheng Wang Cancan Li Lirong Lu A New Algorithm for the Common Solutions of a Generalized Variational Inequality System and a Nonlinear Operator Equation in Banach Spaces Mathematics asymptotically non-expansive mapping general variational inequality system strong convergence Banach space |
| title | A New Algorithm for the Common Solutions of a Generalized Variational Inequality System and a Nonlinear Operator Equation in Banach Spaces |
| title_full | A New Algorithm for the Common Solutions of a Generalized Variational Inequality System and a Nonlinear Operator Equation in Banach Spaces |
| title_fullStr | A New Algorithm for the Common Solutions of a Generalized Variational Inequality System and a Nonlinear Operator Equation in Banach Spaces |
| title_full_unstemmed | A New Algorithm for the Common Solutions of a Generalized Variational Inequality System and a Nonlinear Operator Equation in Banach Spaces |
| title_short | A New Algorithm for the Common Solutions of a Generalized Variational Inequality System and a Nonlinear Operator Equation in Banach Spaces |
| title_sort | new algorithm for the common solutions of a generalized variational inequality system and a nonlinear operator equation in banach spaces |
| topic | asymptotically non-expansive mapping general variational inequality system strong convergence Banach space |
| url | https://www.mdpi.com/2227-7390/8/11/1944 |
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