Well-posedness for parametric strong vector quasi-equilibrium problems with applications

Abstract

In this article, we generalize the concept of well-posedness to the parametric strong vector quasi-equilibrium problem. Under some suitable conditions, we establish some characterizations of well-posedness for parametric strong vector quasiequilibrium problems. The corresponding concept of well-posedness in the generalized sense is also investigated for the parametric strong vector quasiequilibrium problem. As applications, we investigate the well-posedness for strong vector quasi-variational inequality problems and strong vector quasi-optimization problems. 2000 Mathematics subject classification: 49K40; 90C31.

Well-Posedness for Parametric Generalized Strong Vector Quasi-Equilibrium Problem

“…An initial concept of well-posedness introduced by Tykhonov, was given in scalar optimization [1]. In recent years, the well-posedness has been extensively studied by many authors for various equilibrium problems [2][3][4][5][6][7][8][9][10].…”