Existence and stability of solutions for generalized strong vector quasi-equilibrium problem

Abstract

In this paper, we study the generalized strong vector quasi-equilibrium problem without assuming that the dual of the ordering cone has a weak ∗ compact base. We establish an existence theorem of solutions for the generalized strong vector quasi-equilibrium problem by using Kakutani–Fan–Glicksberg fixed point theorem and discuss the closedness of the strong solution set. Moreover, we also derive a stability result for this problem.