New results on systems of generalized vector quasi-equilibrium problems

In this paper, we firstly prove the existence of the equilibrium for the generalized abstract economy. We apply these results to show the existence of solutions for systems of vector quasi-equilibrium problems with multivalued trifunctions. Secondly, we consider the generalized strong vector quasi-equilibrium problems and study the existence of their solutions in the case when the correspondences are weakly naturally quasi-concave or weakly biconvex and also in the case of weak-continuity assumptions. In all situations, fixed-point theorems are used.