The Solvability of Generalized Systems of Time-Dependent Hemivariational Inequalities Enjoying Symmetric Structure in Reflexive Banach Spaces
In real reflexive Banach spaces, let the GSTDHVI, SHVI, DVIP, VIT, and KKM represent a generalized system of time-dependent hemivariational inequalities, a system of hemivariational inequalities, a derived vector inclusion problem, Volterra integral term, and Knaster–Kuratowski–Mazurkiewicz, respect...
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MDPI AG
2021-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/10/1801 |
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| author | Lu-Chuan Ceng Yi-Xuan Fu Jie Yin Liang He Long He Hui-Ying Hu |
| author_facet | Lu-Chuan Ceng Yi-Xuan Fu Jie Yin Liang He Long He Hui-Ying Hu |
| author_sort | Lu-Chuan Ceng |
| collection | DOAJ |
| description | In real reflexive Banach spaces, let the GSTDHVI, SHVI, DVIP, VIT, and KKM represent a generalized system of time-dependent hemivariational inequalities, a system of hemivariational inequalities, a derived vector inclusion problem, Volterra integral term, and Knaster–Kuratowski–Mazurkiewicz, respectively, where the GSTDHVI consists of two parts which are of symmetric structure mutually. By virtue of the surjectivity theorem for pseudo-monotonicity mappings and the Banach contraction mapping principle, instead of the KKM theorems exploited by other authors in recent literature for a SHVI, we consider and study a GSTDHVI with VITs. Under quite mild assumptions, it is shown that there exists only a solution to the investigated problem via demonstrating that a DVIP with VIT is solvable. |
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| id | doaj.art-6e6827c2470e4f33a604217c0b04e941 |
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| language | English |
| last_indexed | 2024-03-10T06:10:27Z |
| publishDate | 2021-09-01 |
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| series | Symmetry |
| spelling | doaj.art-6e6827c2470e4f33a604217c0b04e9412023-11-22T20:09:18ZengMDPI AGSymmetry2073-89942021-09-011310180110.3390/sym13101801The Solvability of Generalized Systems of Time-Dependent Hemivariational Inequalities Enjoying Symmetric Structure in Reflexive Banach SpacesLu-Chuan Ceng0Yi-Xuan Fu1Jie Yin2Liang He3Long He4Hui-Ying Hu5Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaIn real reflexive Banach spaces, let the GSTDHVI, SHVI, DVIP, VIT, and KKM represent a generalized system of time-dependent hemivariational inequalities, a system of hemivariational inequalities, a derived vector inclusion problem, Volterra integral term, and Knaster–Kuratowski–Mazurkiewicz, respectively, where the GSTDHVI consists of two parts which are of symmetric structure mutually. By virtue of the surjectivity theorem for pseudo-monotonicity mappings and the Banach contraction mapping principle, instead of the KKM theorems exploited by other authors in recent literature for a SHVI, we consider and study a GSTDHVI with VITs. Under quite mild assumptions, it is shown that there exists only a solution to the investigated problem via demonstrating that a DVIP with VIT is solvable.https://www.mdpi.com/2073-8994/13/10/1801systems of time-dependent generalized hemivariational inequalitiessymmetric structurepseudo-monotonicity mappingClarke’s generalized directional derivativeBanach contraction mapping principle |
| spellingShingle | Lu-Chuan Ceng Yi-Xuan Fu Jie Yin Liang He Long He Hui-Ying Hu The Solvability of Generalized Systems of Time-Dependent Hemivariational Inequalities Enjoying Symmetric Structure in Reflexive Banach Spaces Symmetry systems of time-dependent generalized hemivariational inequalities symmetric structure pseudo-monotonicity mapping Clarke’s generalized directional derivative Banach contraction mapping principle |
| title | The Solvability of Generalized Systems of Time-Dependent Hemivariational Inequalities Enjoying Symmetric Structure in Reflexive Banach Spaces |
| title_full | The Solvability of Generalized Systems of Time-Dependent Hemivariational Inequalities Enjoying Symmetric Structure in Reflexive Banach Spaces |
| title_fullStr | The Solvability of Generalized Systems of Time-Dependent Hemivariational Inequalities Enjoying Symmetric Structure in Reflexive Banach Spaces |
| title_full_unstemmed | The Solvability of Generalized Systems of Time-Dependent Hemivariational Inequalities Enjoying Symmetric Structure in Reflexive Banach Spaces |
| title_short | The Solvability of Generalized Systems of Time-Dependent Hemivariational Inequalities Enjoying Symmetric Structure in Reflexive Banach Spaces |
| title_sort | solvability of generalized systems of time dependent hemivariational inequalities enjoying symmetric structure in reflexive banach spaces |
| topic | systems of time-dependent generalized hemivariational inequalities symmetric structure pseudo-monotonicity mapping Clarke’s generalized directional derivative Banach contraction mapping principle |
| url | https://www.mdpi.com/2073-8994/13/10/1801 |
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