Inspired by the fact that the discontinuous mappings cannot be (Banach type) contractions and cyclic contractions need not be continuous, and taking into account that there are applications to integral and differential equations based on cyclic contractions, we present results concerning the existence of fixed points for set-valued cyclic operators under implicit relations. Examples are given to support the usability of our results. As an application, we deduce an existence theorem for an integral inclusion. © 2016.