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Article

The Solvability of Generalized Systems of Time-Dependent Hemivariational Inequalities Enjoying Symmetric Structure in Reflexive Banach Spaces

Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
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Author to whom correspondence should be addressed.
Academic Editor: Juan Alberto Rodríguez Velázquez
Symmetry 2021, 13(10), 1801; https://doi.org/10.3390/sym13101801
Received: 8 September 2021 / Revised: 19 September 2021 / Accepted: 23 September 2021 / Published: 27 September 2021
(This article belongs to the Special Issue Nonlinear Analysis and Its Applications in Symmetry)
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. View Full-Text
Keywords: systems of time-dependent generalized hemivariational inequalities; symmetric structure; pseudo-monotonicity mapping; Clarke’s generalized directional derivative; Banach contraction mapping principle systems of time-dependent generalized hemivariational inequalities; symmetric structure; pseudo-monotonicity mapping; Clarke’s generalized directional derivative; Banach contraction mapping principle
MDPI and ACS Style

Ceng, L.-C.; Fu, Y.-X.; Yin, J.; He, L.; He, L.; Hu, H.-Y. The Solvability of Generalized Systems of Time-Dependent Hemivariational Inequalities Enjoying Symmetric Structure in Reflexive Banach Spaces. Symmetry 2021, 13, 1801. https://doi.org/10.3390/sym13101801

AMA Style

Ceng L-C, Fu Y-X, Yin J, He L, He L, Hu H-Y. The Solvability of Generalized Systems of Time-Dependent Hemivariational Inequalities Enjoying Symmetric Structure in Reflexive Banach Spaces. Symmetry. 2021; 13(10):1801. https://doi.org/10.3390/sym13101801

Chicago/Turabian Style

Ceng, Lu-Chuan, Yi-Xuan Fu, Jie Yin, Liang He, Long He, and Hui-Ying Hu. 2021. "The Solvability of Generalized Systems of Time-Dependent Hemivariational Inequalities Enjoying Symmetric Structure in Reflexive Banach Spaces" Symmetry 13, no. 10: 1801. https://doi.org/10.3390/sym13101801

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