A Novel System and Iterative Schemes for Generalized Variational Inclusion Problems and its Approximation Solvability
The variational inclusion problems are the generalizations of the variational inequality problems. First, it was noted by Hasounni and Moudafi in 1994. Afterwards, many researchers look into the problems and try to improve the catch, and then the theory of the variational inclusion problems is enric...
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University of Maragheh
2024-07-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_712160_a3af3db7ef82aab82e32e1dfb0bc666c.pdf |
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| author | Mohd Sarfaraz Md. Kalimuddin Ahmad |
| author_facet | Mohd Sarfaraz Md. Kalimuddin Ahmad |
| author_sort | Mohd Sarfaraz |
| collection | DOAJ |
| description | The variational inclusion problems are the generalizations of the variational inequality problems. First, it was noted by Hasounni and Moudafi in 1994. Afterwards, many researchers look into the problems and try to improve the catch, and then the theory of the variational inclusion problems is enriched from time to time. There were some specific ways of solving the systems of the problems and it is called the approximation solvability of the system, which was due to R. U. Verma in 2008. Here in this study, we investigate the approximation solvability of solutions for the system of generalized nonlinear ordered variational inclusions using an iterative algorithm under some apt conditions. We employ the resolvent operator techniques in our iterative scheme as a baseline. Some exceptional cases of the problem and iterative scheme are also discussed. |
| format | Article |
| id | doaj-art-a32b4679de3e4880a82578e340970f4b |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-a32b4679de3e4880a82578e340970f4b2025-02-11T05:27:31ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-07-0121319721110.22130/scma.2023.2001895.1319712160A Novel System and Iterative Schemes for Generalized Variational Inclusion Problems and its Approximation SolvabilityMohd Sarfaraz0Md. Kalimuddin Ahmad1Department of Mathematics, Jaypee Institute of Information Technology, Noida (Uttar Pradesh), India.Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India.The variational inclusion problems are the generalizations of the variational inequality problems. First, it was noted by Hasounni and Moudafi in 1994. Afterwards, many researchers look into the problems and try to improve the catch, and then the theory of the variational inclusion problems is enriched from time to time. There were some specific ways of solving the systems of the problems and it is called the approximation solvability of the system, which was due to R. U. Verma in 2008. Here in this study, we investigate the approximation solvability of solutions for the system of generalized nonlinear ordered variational inclusions using an iterative algorithm under some apt conditions. We employ the resolvent operator techniques in our iterative scheme as a baseline. Some exceptional cases of the problem and iterative scheme are also discussed.https://scma.maragheh.ac.ir/article_712160_a3af3db7ef82aab82e32e1dfb0bc666c.pdfsolvabilitygvipapproximationexistence |
| spellingShingle | Mohd Sarfaraz Md. Kalimuddin Ahmad A Novel System and Iterative Schemes for Generalized Variational Inclusion Problems and its Approximation Solvability Sahand Communications in Mathematical Analysis solvability gvip approximation existence |
| title | A Novel System and Iterative Schemes for Generalized Variational Inclusion Problems and its Approximation Solvability |
| title_full | A Novel System and Iterative Schemes for Generalized Variational Inclusion Problems and its Approximation Solvability |
| title_fullStr | A Novel System and Iterative Schemes for Generalized Variational Inclusion Problems and its Approximation Solvability |
| title_full_unstemmed | A Novel System and Iterative Schemes for Generalized Variational Inclusion Problems and its Approximation Solvability |
| title_short | A Novel System and Iterative Schemes for Generalized Variational Inclusion Problems and its Approximation Solvability |
| title_sort | novel system and iterative schemes for generalized variational inclusion problems and its approximation solvability |
| topic | solvability gvip approximation existence |
| url | https://scma.maragheh.ac.ir/article_712160_a3af3db7ef82aab82e32e1dfb0bc666c.pdf |
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