Vector Equilibrium Problems on Dense Sets

In this paper, we provide sufficient conditions that ensure the existence of the solution of some vector equilibrium problems in Hausdorff topological vector spaces ordered by a cone. The conditions that we consider are imposed not on the whole domain of the operators involved, but rather on a self-segment-dense subset of it, a special type of dense subset. We apply the obtained results to vector optimization and vector variational inequalities.

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