Fixed points of ordered F-contractions

In his recent paper, Wardowski [16] introduced the concept of F-contraction, which is a proper generalization of ordinary contraction on a complete metric space. Then, some generalizations of F-contractions including multivalued case are obtained in [2, 4, 7, 13]. In this paper, by considering both F-contractions and fixed point result on ordered metric spaces, we introduce a new concept of ordered F-contraction on ordered metric space. Then, we give a fixed point theorem for such mapping. To support our result, we give an example showing that our main theorem is applicable, but both results of Ran and Reurings [12] and Wardowski [16] are not.