The generalized vector quasi-variational-like inequalities

In this paper, we introduce and study a class of Generalized Vector Quasi-Variational-Like Inequality Problem (GVQVLIP) involving set-valued mappings with certain monotonicity. By employing the scalarization technique, several existence results for solutions of the (GVQVLIP) are established under noncompact setting in topological vector spaces. These new existence results improve, unify, and generalize many known results for scalar and vector variational inequalities in recent literature.