In this paper we provide some new sufficient conditions that ensure the
existence of the solution of a weak vector equilibrium problem in Hausdorff
topological vector spaces ordered by a cone. Further, we introduce a dual
problem and we provide conditions that assure the solution set of the original
problem and its dual coincide. We show that many known problems from the
literature can be treated in our primal-dual model. We provide several
coercivity conditions in order to obtain solution existence of the primal-dual
problems without compactness assumption. We pay a special attention to the case
when the base space is a reflexive Banach space. We apply the results obtained
to perturbed vector equilibrium problems.Comment: 20 page