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