Existence of Solutions to Generalized Vector Quasi-Variational-Like Inequalities with Set-Valued Mappings (Communications in Mathematical Research, 2021)
In this paper, we introduce and study a class of generalized vector quasi-variational-like inequality problems, which includes generalized nonlinear vector variational inequality problems, generalized vector variational inequality problems andgeneralized vector variational-like inequality problems as special cases. We use themaximal element theorem with an escaping sequence to prove the existence results ofa solution for generalized vector quasi-variational-like inequalities without any monotonicity conditions in the setting of locally convex topological vector space.
Keywords: generalized vector quasi-variational-like inequality; maximal element theorem; upper semicontinuous diagonal convexity; locally convex topological vector space.