Existence of solutions of systems of generalized implicit vector quasi-equilibrium problems

We consider five different types of systems of generalized vector quasi-equilibrium problems and establish relationships among them by using different kinds of generalized pseudomonotonicities. We prove the existence of their solutions under lower semicontinuity for a family of multivalued maps involved in the formulation of these problems. The existence of solutions of these problems is also investigated without any coercivity condition but for Φ-condensing maps. We also establish some existence results for solutions of these problems under pseudomonotonicities in the setting of Hausdorff topological vector spaces as well as real Banach spaces.