Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert Spaces
In this paper, we establish an iterative algorithm by combining Yamada’s hybrid steepest descent method and Wang’s algorithm for finding the common solutions of variational inequality problems and split feasibility problems. The strong convergence of the sequence generated by our suggested iterative...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2021/9980309 |
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| author | Panisa Lohawech Anchalee Kaewcharoen Ali Farajzadeh |
| author_facet | Panisa Lohawech Anchalee Kaewcharoen Ali Farajzadeh |
| author_sort | Panisa Lohawech |
| collection | DOAJ |
| description | In this paper, we establish an iterative algorithm by combining Yamada’s hybrid steepest descent method and Wang’s algorithm for finding the common solutions of variational inequality problems and split feasibility problems. The strong convergence of the sequence generated by our suggested iterative algorithm to such a common solution is proved in the setting of Hilbert spaces under some suitable assumptions imposed on the parameters. Moreover, we propose iterative algorithms for finding the common solutions of variational inequality problems and multiple-sets split feasibility problems. Finally, we also give numerical examples for illustrating our algorithms. |
| format | Article |
| id | doaj-art-1a53e21b2a7148a280c117565d7ee125 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1a53e21b2a7148a280c117565d7ee1252025-02-03T01:25:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252021-01-01202110.1155/2021/99803099980309Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert SpacesPanisa Lohawech0Anchalee Kaewcharoen1Ali Farajzadeh2Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandDepartment of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandDepartment of Mathematics, Faculty of Science, Razi University, Kermanshah 67146, IranIn this paper, we establish an iterative algorithm by combining Yamada’s hybrid steepest descent method and Wang’s algorithm for finding the common solutions of variational inequality problems and split feasibility problems. The strong convergence of the sequence generated by our suggested iterative algorithm to such a common solution is proved in the setting of Hilbert spaces under some suitable assumptions imposed on the parameters. Moreover, we propose iterative algorithms for finding the common solutions of variational inequality problems and multiple-sets split feasibility problems. Finally, we also give numerical examples for illustrating our algorithms.http://dx.doi.org/10.1155/2021/9980309 |
| spellingShingle | Panisa Lohawech Anchalee Kaewcharoen Ali Farajzadeh Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert Spaces International Journal of Mathematics and Mathematical Sciences |
| title | Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert Spaces |
| title_full | Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert Spaces |
| title_fullStr | Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert Spaces |
| title_full_unstemmed | Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert Spaces |
| title_short | Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert Spaces |
| title_sort | convergence theorems for the variational inequality problems and split feasibility problems in hilbert spaces |
| url | http://dx.doi.org/10.1155/2021/9980309 |
| work_keys_str_mv | AT panisalohawech convergencetheoremsforthevariationalinequalityproblemsandsplitfeasibilityproblemsinhilbertspaces AT anchaleekaewcharoen convergencetheoremsforthevariationalinequalityproblemsandsplitfeasibilityproblemsinhilbertspaces AT alifarajzadeh convergencetheoremsforthevariationalinequalityproblemsandsplitfeasibilityproblemsinhilbertspaces |