Metric Characterizations of α -Well-Posedness for a System ofMixed Quasivariational-Like Inequalities in Banach Spaces

Abstract

The purpose of this paper is to investigate the problems of the well-posednessfor a system of mixed quasivariational-like inequalities in Banach spaces. First, we generalize the concept of $\alpha$-well-posedness to the system of mixed quasivariational-like inequalities,which includes symmetric quasi-equilibrium problems as a special case. Second, we establishsome metric characterizations of $\alpha$-well-posedness for the system of mixed quasivariational-likeinequalities. Under some suitable conditions, we prove that the $\alpha$-well-posedness is equivalent to the existence and uniqueness of solution for the system of mixed quasivariational-likeinequalities. The corresponding concept of $\alpha$-well-posedness in the generalized sense is alsoconsidered for the system of mixed quasivariational-like inequalities having more than onesolution. The results presented in this paper generalize and improve some known results inthe literature.