Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational Inequalities
In this article, we consider and study a system of generalized set-valued variational inequalities involving relaxed cocoercive mappings in Hilbert spaces. Using the projection method and Banach contraction principle, we prove the existence of a solution for the considered problem. Further, we propo...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/6674349 |
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| author | M. Akram Aysha Khan M. Dilshad |
| author_facet | M. Akram Aysha Khan M. Dilshad |
| author_sort | M. Akram |
| collection | DOAJ |
| description | In this article, we consider and study a system of generalized set-valued variational inequalities involving relaxed cocoercive mappings in Hilbert spaces. Using the projection method and Banach contraction principle, we prove the existence of a solution for the considered problem. Further, we propose an iterative algorithm and discuss its convergence. Moreover, we establish equivalence between the system of variational inequalities and altering points problem. Some parallel iterative algorithms are proposed, and the strong convergence of the sequences generated by these iterative algorithms is discussed. Finally, a numerical example is constructed to illustrate the convergence analysis of the proposed parallel iterative algorithms. |
| format | Article |
| id | doaj-art-e9cff98c7d9d4f708a8134e7500b2878 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-e9cff98c7d9d4f708a8134e7500b28782025-02-03T01:05:27ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/66743496674349Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational InequalitiesM. Akram0Aysha Khan1M. Dilshad2Department of Mathematics, Faculty of Science, Islamic University of Madinah, Saudi ArabiaCollege of Arts and Science, Wadi Addwasir, Prince Sattam bin Abdulaziz University, Al-Kharj, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Tabuk, Saudi ArabiaIn this article, we consider and study a system of generalized set-valued variational inequalities involving relaxed cocoercive mappings in Hilbert spaces. Using the projection method and Banach contraction principle, we prove the existence of a solution for the considered problem. Further, we propose an iterative algorithm and discuss its convergence. Moreover, we establish equivalence between the system of variational inequalities and altering points problem. Some parallel iterative algorithms are proposed, and the strong convergence of the sequences generated by these iterative algorithms is discussed. Finally, a numerical example is constructed to illustrate the convergence analysis of the proposed parallel iterative algorithms.http://dx.doi.org/10.1155/2021/6674349 |
| spellingShingle | M. Akram Aysha Khan M. Dilshad Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational Inequalities Journal of Function Spaces |
| title | Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational Inequalities |
| title_full | Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational Inequalities |
| title_fullStr | Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational Inequalities |
| title_full_unstemmed | Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational Inequalities |
| title_short | Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational Inequalities |
| title_sort | convergence of some iterative algorithms for system of generalized set valued variational inequalities |
| url | http://dx.doi.org/10.1155/2021/6674349 |
| work_keys_str_mv | AT makram convergenceofsomeiterativealgorithmsforsystemofgeneralizedsetvaluedvariationalinequalities AT ayshakhan convergenceofsomeiterativealgorithmsforsystemofgeneralizedsetvaluedvariationalinequalities AT mdilshad convergenceofsomeiterativealgorithmsforsystemofgeneralizedsetvaluedvariationalinequalities |