$\alpha$-Well posedness by perturbations of split quasi-equilibrium problems in Banach spaces

Abstract

Zolezzi introduced the notion of well-posedness by perturbations for the minimization problem. In this paper, we extend this concept to Levitin-Polyak $\alpha$-well-posedness by perturbations for split quasi-equilibrium problems in real Banach spaces. We establish some metric characterization results between the (generalized) $\alpha$-well-posedness by perturbations for split quasi-equilibrium problems and their solution set. Moreover, we derive some conditions under which the $\alpha$-well-posedness by perturbations of a split quasi-equilibrium problem is equivalent to the existence and uniqueness of its solution.