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

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1801
Author(s):  
Lu-Chuan Ceng ◽  
Yi-Xuan Fu ◽  
Jie Yin ◽  
Liang He ◽  
Long He ◽  
...  
Keyword(s):  
Banach Spaces ◽  
Contraction Mapping Principle ◽  
Time Dependent ◽  
Inclusion Problem ◽  
Hemivariational Inequalities ◽  
Reflexive Banach Spaces ◽  
Generalized System ◽  
Symmetric Structure ◽  
Generalized Systems ◽  
Banach Contraction

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.

scholarly journals Well-posedness for generalized variational-hemivariational inequalities with perturbations in reflexive banach spaces

2017 ◽  
Vol 48 (4) ◽  
pp. 345-364 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Yung-Yih Lur ◽  
Ching-Feng Wen
Keyword(s):  
Banach Spaces ◽  
Minimization Problem ◽  
Hemivariational Inequality ◽  
Inclusion Problem ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Reflexive Banach Spaces ◽  
Mild Conditions ◽  
Well Posed

In this paper, we consider an extension of well-posedness for a minimization problem to a class of generalized variational-hemivariational inequalities with perturbations in reflexive Banach spaces. We establish some metric characterizations for the $\alpha$-well-posed generalized variational-hemivariational inequality and give some conditions under which the generalized variational-hemivariational inequality is strongly $\alpha$-well-posed in the generalized sense. Under some mild conditions, we also prove the equivalence between the $\alpha$-well-posedness of the generalized variational-hemivariational inequality and the $\alpha$-well-posedness of the corresponding inclusion problem.

scholarly journals Nonlocal Cauchy Problem via a Fractional Operator Involving Power Kernel in Banach Spaces

2019 ◽  
Vol 3 (2) ◽  
pp. 27 ◽  
Author(s):  
Ayşegül Keten ◽  
Mehmet Yavuz ◽  
Dumitru Baleanu
Keyword(s):  
Banach Spaces ◽  
Fractional Derivatives ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Kernel Functions ◽  
Banach Contraction ◽  
Exponential Decay Law ◽  
Nonlocal Cauchy Problem ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

We investigated existence and uniqueness conditions of solutions of a nonlinear differential equation containing the Caputo–Fabrizio operator in Banach spaces. The mentioned derivative has been proposed by using the exponential decay law and hence it removed the computational complexities arising from the singular kernel functions inherit in the conventional fractional derivatives. The method used in this study is based on the Banach contraction mapping principle. Moreover, we gave a numerical example which shows the applicability of the obtained results.

scholarly journals A Class of Variational-Hemivariational Inequalities in Reflexive Banach Spaces

2016 ◽  
Vol 127 (2) ◽  
pp. 151-178 ◽  
Author(s):  
Stanisław Migórski ◽  
Anna Ochal ◽  
Mircea Sofonea
Keyword(s):  
Banach Spaces ◽  
Hemivariational Inequalities ◽  
Reflexive Banach Spaces

scholarly journals Well-posedness for systems of time-dependent hemivariational inequalities in Banach spaces

2017 ◽  
Vol 10 (08) ◽  
pp. 4318-4336 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Yeong-Cheng Liou ◽  
Jen-Chih Yao ◽  
Yonghong Yao
Keyword(s):  
Banach Spaces ◽  
Time Dependent ◽  
Hemivariational Inequalities ◽  
Well Posedness

scholarly journals Positive Solutions for Nonlinear Integro-Differential Equations of Mixed Type in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Yan Sun
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Positive Solutions ◽  
Existence Theorems ◽  
Contraction Mapping Principle ◽  
Equations Of Mixed Type ◽  
Comparison Results ◽  
Banach Contraction ◽  
Banach Contraction Mapping Principle ◽  
Ordered Banach Spaces

We establish some new existence theorems on the positive solutions for nonlinear integro-differential equations which do not possess any monotone properties in ordered Banach spaces by means of Banach contraction mapping principle and cone theory based on some new comparison results.

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