Metric characterizations of \(\alpha \)-well-posedness for symmetric quasi-equilibrium problems (Q1037374)

In this paper, the authors generalize the concept of \(\alpha\)-well-posedness to the symmetric quasi-equilibrium problems which includes equilibrium problems, Nash equilibrium problems, quasi-variational inequalities, variational inequalities and fixed point problems as special cases. Some metric characterizations of \(\alpha\)-well-posedness for symmetric quasi-equilibrium problems are given under some suitable conditions. The authors also prove that the \(\alpha\)-well-posedness is equivalent to the existence and uniqueness of solutions for the symmetric quasi-equilibrium problems under some suitable conditions. The corresponding concept of \(\alpha\)-well-posedness in the generalized sense is also investigated for the symmetric quasi-equilibrium problem having more than one solution.