With A Function Constraint (vector) (generalized) Levitin,-polyak, Proposed Variational Inequalities Posedness

In this paper, we introduce Levtin-Polyak type well-posedness for quasivariational inequality problems with functional constraints, generalized quasivariational inequality problems with functional constraints, and vector quasivariational inequality problems with functional constraints. Some necessary and/or sufficient conditions are derived for them. Finally, we establish an equivalence between a vector variational inequality and a (scalar) generalized variational inequality and the equivalence between a vector quasivariational inequality and a (scalar) generalized quasivariational inequality. We also show that Levtin-polyak well-posedness of a vector variational inequality is equivalent to that of a (scalar) generalized variational inequality and the same equivalence between Levtin-polyak well-posedness of a vector quasivariational inequality and that of a (scalar) generalized quasivariational inequality.