Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures
In this paper, two types of set-valued symmetric generalized strong vector quasi-equilibrium problems with variable ordering structures are discussed. By using the concept of cosmically upper continuity rather than the one of upper semicontinuity for cone-valued mapping, some existence theorems of s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/9/1604 |
| _version_ | 1827706009037045760 |
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| author | Jing-Nan Li San-Hua Wang Yu-Ping Xu |
| author_facet | Jing-Nan Li San-Hua Wang Yu-Ping Xu |
| author_sort | Jing-Nan Li |
| collection | DOAJ |
| description | In this paper, two types of set-valued symmetric generalized strong vector quasi-equilibrium problems with variable ordering structures are discussed. By using the concept of cosmically upper continuity rather than the one of upper semicontinuity for cone-valued mapping, some existence theorems of solutions are established under suitable assumptions of cone-continuity and cone-convexity for the equilibrium mappings. Moreover, the results of compactness for solution sets are proven. As applications, some existence results of strong saddle points are obtained. The main results obtained in this paper unify and improve some recent works in the literature. |
| first_indexed | 2024-03-10T16:15:37Z |
| format | Article |
| id | doaj.art-6061a220f70e4219825745d6d0929bf5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T16:15:37Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6061a220f70e4219825745d6d0929bf52023-11-20T14:04:52ZengMDPI AGMathematics2227-73902020-09-0189160410.3390/math8091604Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering StructuresJing-Nan Li0San-Hua Wang1Yu-Ping Xu2Department of Mathematics, Nanchang University, Nanchang 330031, ChinaDepartment of Mathematics, Nanchang University, Nanchang 330031, ChinaDepartment of Mathematics, Nanchang University, Nanchang 330031, ChinaIn this paper, two types of set-valued symmetric generalized strong vector quasi-equilibrium problems with variable ordering structures are discussed. By using the concept of cosmically upper continuity rather than the one of upper semicontinuity for cone-valued mapping, some existence theorems of solutions are established under suitable assumptions of cone-continuity and cone-convexity for the equilibrium mappings. Moreover, the results of compactness for solution sets are proven. As applications, some existence results of strong saddle points are obtained. The main results obtained in this paper unify and improve some recent works in the literature.https://www.mdpi.com/2227-7390/8/9/1604symmetric generalized strong vector quasi-equilibrium problemsvariable ordering structuresexistence of solutionscosmically upper continuityfixed point theorem |
| spellingShingle | Jing-Nan Li San-Hua Wang Yu-Ping Xu Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures Mathematics symmetric generalized strong vector quasi-equilibrium problems variable ordering structures existence of solutions cosmically upper continuity fixed point theorem |
| title | Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures |
| title_full | Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures |
| title_fullStr | Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures |
| title_full_unstemmed | Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures |
| title_short | Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures |
| title_sort | set valued symmetric generalized strong vector quasi equilibrium problems with variable ordering structures |
| topic | symmetric generalized strong vector quasi-equilibrium problems variable ordering structures existence of solutions cosmically upper continuity fixed point theorem |
| url | https://www.mdpi.com/2227-7390/8/9/1604 |
| work_keys_str_mv | AT jingnanli setvaluedsymmetricgeneralizedstrongvectorquasiequilibriumproblemswithvariableorderingstructures AT sanhuawang setvaluedsymmetricgeneralizedstrongvectorquasiequilibriumproblemswithvariableorderingstructures AT yupingxu setvaluedsymmetricgeneralizedstrongvectorquasiequilibriumproblemswithvariableorderingstructures |