Levitin-polyak well-posedness for symmetric weak vector quasi-equilibrium problems

. In this paper, we consider symmetric weak vector quasi-equilibrium problems and introduce the concepts of Levitin-Polyak well-posedness and LevitinPolyak well-posedness in the generalized sense for these problems. Then, we show that, under suitable conditions, the equivalence between the Levitin-Polyak well-posedness properties and the existence of solutions for the considered problem is given. Further, some metric characterizations of the Levitin-Polyak wellposedness and Levitin-Polyak well-posedness in the generalized sense for such problems in terms of the behavior of the approximate solution sets are also discussed. Finally, as an application, we study the special case of symmetric weak vector quasi-variational inequality problems. The results presented in this paper improve and extend some main results in the literature. Some examples are given for the illustration of our results.