<p>The main purpose of this paper is to study Hölder continuity of solution maps in parametric equilibrium problems defined by trifunctions under perturbation of both the objective function and the constraints set. As application, we give some results on Hölder continuity for parametric mixed equilibrium problems and parametric variational inequalities. In addition, we discuss the case of time-dependent variational inequality problems in which the constraints set depends on time that also enters as a parameter in the variational formulation. Our results are new and may be exploited to derive valuable stability results for optimization problems, variational and hemi-variational inequalities and many other related problems.</p>