Equivalence of well-posedness between systems of hemivariational inequalities and inclusion problems

Abstract

In this paper, we generalize the concept of well-posedness to a system of hemivariational inequalities in Banach space. By introducing several concepts of well-posedness for systems of hemivariational inequalities considered, we establish some metric characterizations of well-posedness and prove some equivalence results of strong (generalized) well-posedness between a system of hemivariational inequalities and its derived system of inclusion problems.

On the characterization of the solution set for vector equilibrium problem

“…In this subsection, we establish the equivalence between the nonemptiness and compactness of the solution set for (VEP) and Levitin-Polyak well-posedness for (VEP) under mild conditions, which generalizes and extends some results of [2,22,28,30,32] in some sense.…”

“…One of the most important problems for (VEP) is to investigate the properties of the solution set, such as existence and uniqueness [11-13, 25-27, 31], semicontinuity and sensitivity [1,7], well-posedness [2,22,[28][29][30]32] and connectedness [16,17,23]. Among many desirable properties of the solution set, the issue of the nonemptiness and boundedness of the solution set is interesting and important, as it can guarantee the convergence of some solution algorithms (see, e.g., [21,33,34]).…”

Solvability of Some Perturbed Generalized Variational Inequalities in Reflexive Banach Spaces

“…The variational inequalities have been widely studied by many authors in recent years; see [12][13][14][15][16][17][18]. One of the most interesting subjects in the theoretical aspect is the research of properties for variational inequalities under data perturbation [19][20][21][22][23][24][25][26][27].…”

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

“…Till now, there are a few papers discussing the solvability of systems of hemivariational inequalities since, due to the complex structure of systems of hemivariational inequalities, it is much more difficult than the study of hemivariational inequalities. Very recently, Wang et al [32] introduced and considered the well-posedness for systems of hemivariational inequalities, gave some metric characterizations of well-posedness and established the equivalence between well-posedness of a system of hemivariational inequalities and its derived system of inclusion problems.…”

“…Inspired by the above research work of [32], in this paper we generalize the notion of α-well-posedness to a system of time-dependent hemivariational inequalities without Volterra integral terms, establish some metric characterizations of α-well-posedness and prove the equivalence between α-well-posedness of the system of time-dependent hemivariational inequalities and its derived system of inclusion problems. The paper is structured as follows.…”