Existence of Solutions to Generalized Vector Quasi-equilibrium Problems with Set-Valued Mappings

Abstract

In this paper, we introduce and study a class of generalized vector quasi-equilibrium problems, which includes generalized vector quasi-variational-like inequality problems, generalized vector equilibrium problems, generalized vector variational inequality problems as special cases. We use the maximal element theorem with an escaping sequence to prove the existence results of solutions for the class of generalized vector quasi-equilibrium problems without any monotonicity conditions in the setting of locally convex topological vector space. The results presented here improve and extend the corresponding results in this area. Keywords-generalized vector quasi-equilibrium problem; maximal element theorem; upper semicontinuity; diagonal convexity; escaping sequence