In this paper, we first propose some kinds ofthe strong convexity (concavity) for vector functions. Thenwe applythese assumptionsto establish sufficient conditions for the Hölder continuity of solution maps of the vector primal and dual equilibrium problems in metric linear spaces. As applications, we derive the Hölder continuity of solution maps of vector optimization problems and vector variational inequalities. Our results improve and generalize some recent existing ones in the literature.