The generalized Tykhonov well-posedness for system of vector quasi-equilibrium problems

Abstract

In this paper, the notion of the generalized Tykhonov well-posedness for system of vector quasi-equilibrium problems are investigated. By using the gap functions of the system of vector quasi-equilibrium problems, we establish the equivalent relationship between the generalized Tykhonov well-posedness of the system of vector quasi-equilibrium problems and that of the minimization problems. We also present some metric characterizations for the generalized Tykhonov well-posedness of the system of vector quasi-equilibrium problems. The results in this paper are new and extend some known results in the literature.

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

“…Also, they established the metric characterizations for well-posed variational inequalities, the necessary and sufficient conditions of well-posedness for variational inequalities, and the links of well-posedness between variational inequalities and their related problems such as minimization problems, fixed pointed problems and inclusion problems. For further results on the well-posedness of variational inequalities, we refer to [10,12,13,23,33] and the references therein.…”

Levitin-Polyak well-posedness of generalized vector quasi-equilibrium problems with functional constraints

“…(iv) there exists 0 < δ 1 < δ 0 such that φ is level-compact on X 1 (δ 1 ) defined by (35); Then (GVQEP) is type I LP well-posed.…”

“…Peng et al [34] introduced and studied four types of Levitin-Polyak well-posedness of vector equilibrium problems with abstract set constraints and functional constraints. Peng and Wu [35] introduced and researched the generalized Tykhonov well-posedness for system of vector quasi-equilibrium problems.…”

On the well-posedness of generalized hemivariational inequalities and inclusion problems in Banach spaces

“…Moreover, they established the metric characterizations for well-posed variational inequalities, the necessary and sufficient conditions of well-posedness for variational inequalities, and the links of well-posedness between variational inequalities and their related problems such as minimization problems, fixed pointed problems and inclusion problems. We refer the readers there to [4,13,15,18,27,[29][30][31]33] for a wealth of additional information on wellposedness for variational inequalities.…”