Perturbed Mixed Variational-like Inequalities and Auxiliary Principle Pertaining to a Fuzzy Environment
Convex and non-convex fuzzy mappings are well known to be important in the research of fuzzy optimization. Symmetry and the idea of convexity are closely related. Therefore, the concept of symmetry and convexity is important in the discussion of inequalities because of how its definition behaves. Th...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/12/2503 |
| _version_ | 1797455187986612224 |
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| author | Muhammad Bilal Khan Gustavo Santos-García Savin Treanțǎ Muhammad Aslam Noor Mohamed S. Soliman |
| author_facet | Muhammad Bilal Khan Gustavo Santos-García Savin Treanțǎ Muhammad Aslam Noor Mohamed S. Soliman |
| author_sort | Muhammad Bilal Khan |
| collection | DOAJ |
| description | Convex and non-convex fuzzy mappings are well known to be important in the research of fuzzy optimization. Symmetry and the idea of convexity are closely related. Therefore, the concept of symmetry and convexity is important in the discussion of inequalities because of how its definition behaves. This study aims to consider new class of generalized fuzzy variational-like inequality for fuzzy mapping which is known as perturbed fuzzy mixed variational-like inequality. We also introduce strongly fuzzy mixed variational inequality, as a particular case of perturbed fuzzy mixed variational-like inequality which is also a new one. Furthermore, by using the generalized auxiliary principle technique and some new analytic techniques, some existence results and efficient numerical techniques of perturbed fuzzy mixed variational-like inequality are established. As exceptional cases, some known and new results are obtained. Results obtained in this paper can be viewed as refinement and improvement of previously known results. |
| first_indexed | 2024-03-09T15:48:53Z |
| format | Article |
| id | doaj.art-a02732a13ae74a07ab4eca8fc6c2bb98 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T15:48:53Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a02732a13ae74a07ab4eca8fc6c2bb982023-11-24T18:18:53ZengMDPI AGSymmetry2073-89942022-11-011412250310.3390/sym14122503Perturbed Mixed Variational-like Inequalities and Auxiliary Principle Pertaining to a Fuzzy EnvironmentMuhammad Bilal Khan0Gustavo Santos-García1Savin Treanțǎ2Muhammad Aslam Noor3Mohamed S. Soliman4Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, PakistanFacultad de Economía y Empresa and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, 37007 Salamanca, SpainDepartment of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, RomaniaDepartment of Mathematics, COMSATS University Islamabad, Islamabad 44000, PakistanDepartment of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaConvex and non-convex fuzzy mappings are well known to be important in the research of fuzzy optimization. Symmetry and the idea of convexity are closely related. Therefore, the concept of symmetry and convexity is important in the discussion of inequalities because of how its definition behaves. This study aims to consider new class of generalized fuzzy variational-like inequality for fuzzy mapping which is known as perturbed fuzzy mixed variational-like inequality. We also introduce strongly fuzzy mixed variational inequality, as a particular case of perturbed fuzzy mixed variational-like inequality which is also a new one. Furthermore, by using the generalized auxiliary principle technique and some new analytic techniques, some existence results and efficient numerical techniques of perturbed fuzzy mixed variational-like inequality are established. As exceptional cases, some known and new results are obtained. Results obtained in this paper can be viewed as refinement and improvement of previously known results.https://www.mdpi.com/2073-8994/14/12/2503fuzzy mappingsperturbed fuzzy mixed variational-like inequalityauxiliary principle techniqueexistenceiterative method |
| spellingShingle | Muhammad Bilal Khan Gustavo Santos-García Savin Treanțǎ Muhammad Aslam Noor Mohamed S. Soliman Perturbed Mixed Variational-like Inequalities and Auxiliary Principle Pertaining to a Fuzzy Environment Symmetry fuzzy mappings perturbed fuzzy mixed variational-like inequality auxiliary principle technique existence iterative method |
| title | Perturbed Mixed Variational-like Inequalities and Auxiliary Principle Pertaining to a Fuzzy Environment |
| title_full | Perturbed Mixed Variational-like Inequalities and Auxiliary Principle Pertaining to a Fuzzy Environment |
| title_fullStr | Perturbed Mixed Variational-like Inequalities and Auxiliary Principle Pertaining to a Fuzzy Environment |
| title_full_unstemmed | Perturbed Mixed Variational-like Inequalities and Auxiliary Principle Pertaining to a Fuzzy Environment |
| title_short | Perturbed Mixed Variational-like Inequalities and Auxiliary Principle Pertaining to a Fuzzy Environment |
| title_sort | perturbed mixed variational like inequalities and auxiliary principle pertaining to a fuzzy environment |
| topic | fuzzy mappings perturbed fuzzy mixed variational-like inequality auxiliary principle technique existence iterative method |
| url | https://www.mdpi.com/2073-8994/14/12/2503 |
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