In this paper, we define the cyclic-Prešić–Ćirić operators in metric-like spaces and prove some fixed point results for such operators. Our results generalize that of S.B. Prešić [Sur une classe d'inéquations aux différences finite et sur la convergence de certaines suites, Publications de l'Institut Mathématique (N.S.), 5(19):75–78, 1965] and several later results. An example is given which shows that the results proved herein are the proper generalizations of existing ones.