Well-posedness of Hemivariational Inequalities and Inclusion Problems

In this article, we investigate the nonemptiness and compactness of the solution set for vector equilibrium problem defined in finite-dimensional spaces. We show that vector equilibrium problem has nonempty and compact solution set if and only if linearly scalarized equilibrium problem has nonempty and compact solution set provided that R 1 = {0} holds. Furthermore, we obtain that vector equilibrium problem has nonempty and compact solution set if and only if linearly scalarized equilibrium problem has nonempty and compact solution set when coercivity condition holds. As applications, we employ the obtained results to derive Levitin-Polyak well-posedness, stability analysis and connectedness of the solution set of the vector equilibrium problem.

Section: Levitin-polyak Well-posedness For (Vep)supporting

confidence: 54%

Section: Introductionmentioning

confidence: 99%

On the characterization of the solution set for vector equilibrium problem

Wang¹,

Gao²

2017

“…Many famous results have been obtained by many distinguished researchers (refer to [17,18,20,22] for details). The concept of well-posedness for hemivariational inequalities was firstly introduced by Goeleven and Mentagui [7] in 1995 and, further, studied by Xiao, Yang and Huang in [23,24,25]. Also, there are a few papers studying 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.…”

Section: Introductionmentioning

confidence: 99%

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

Wang¹,

Xiao²,

Wang³

et al. 2016

Self Cite

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.

“…In 1995, Goeleven and Mentagui [13] first introduced the well-posedness for a hemivariational inequality and presented some basic results concerning the well-posed hemivariational inequality. Later, using the concept of approximating sequence, Xiao et al [34,36] defined a concept of well-posedness for a hemivariational inequality and a variational-hemivariational inequality. They gave some metric characterizations for the well-posed hemivariational inequality and the well-posed variational-hemivariational inequality, and proved the equivalence of well-posedness between the hemivariational inequality and the corresponding inclusion problem.…”

Section: Introductionmentioning

confidence: 99%

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

Ceng¹,

Liou²,

Yao³

et al. 2017

In this paper, we generalize the concept of α-well-posedness to a system of time-dependent hemivariational inequalities without Volterra integral terms in Banach spaces. We establish some metric characterizations of α-well-posedness and prove some equivalence results of strong α-well-posedness (resp., in the generalized sense) between a system of time-dependent hemivariational inequalities and its derived system of inclusion problems.