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By applying hybrid inclusion and disclusion systems (HIDS), we establish several vectorial variantsof system of Ekeland's variational principle on topological vector spaces, some existence theorems of system of parametric vectorial quasi-equilibriumproblem, and an existence theorem of system of the Stampacchia-type vectorial equilibrium problem. As an application, a vectorial minimization theorem isalso given. Moreover, we discuss some equivalence relations between our vectorial variant of Ekeland's variational principle, common fixed pointtheorem, and maximal element theorem

Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization Problems