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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Published in:Symmetry (Basel) 2021-10, Vol.13 (10), p.1801
Main Authors: Ceng, Lu-Chuan, Fu, Yi-Xuan, Yin, Jie, He, Liang, He, Long, Hu, Hui-Ying
Format: Article
Language:English
Subjects:
Banach contraction mapping principle
Banach spaces
Clarke’s generalized directional derivative
Inequalities
Inequality
pseudo-monotonicity mapping
symmetric structure
systems of time-dependent generalized hemivariational inequalities
Theorems
Time dependence
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym13101801