Available online at www.isr-publications.com/jmcs J. Math. Computer Sci., 17 (2017), 32–40 Research Article Journal Homepage: www.tjmcs.com - www.isr-publications.com/jmcs F-contraction on asymmetric metric spaces Hossein Piri a , Samira Rahrovi a , Hamidreza Marasi a , Poom Kumam b,c,d,* a Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, 5551761167, Iran. b KMUTT Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand. c KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand. d Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan. Abstract In this paper, we introduce the notion of an F-contraction in the setting of complete asymmetric metric spaces and we investigate the existence of fixed points of such mappings. Our results unify, extend, and improve several results in the literature. c 2017 All rights reserved. Keywords: Fixed point, asymmetric metric spaces, F-contraction. 2010 MSC: 74H10, 54H25. 1. Introduction In 1931, for the first time asymmetric metric spaces were introduced by Wilson [16] as quasi-metric spaces, and then studied by many authors (see [1, 6, 8, 11]). An asymmetric metric space is a gener- alization of a metric space, but without the requirement that the (asymmetric) metric ρ has to satisfy ρ(x, y)= ρ(y, x). In asymmetric metric spaces some notions, such as convergence, compactness and com- pleteness are different from this in metric case. There are two notions for each of them, namely forward and backward ones, since we have two topologies which are the forward topology and the backward topology in asymmetric metric spaces (see [5]). Collins and Zimmer [2] studied these notions in the asymmetric context. Asymmetric metrics have many applications in pure and applied mathematics; for example, asymmetric metric spaces have recently been studied with questions of existence and uniqueness of Hamilton-Jacobi equations [8] in mind. In recent years an interesting but different generalizations of the Banach-contraction theorem have been given by Wardowski [14]. This result have become of recent interest of many authors (see [3, 4, 10, 12, 13, 15] and references therein). * Corresponding author Email addresses: h.piri@bonabu.ac.ir (Hossein Piri), s.rahrovi@bonabu.ac.ir (Samira Rahrovi), hamidreza.marasi@gmail.com (Hamidreza Marasi), poom.kumam@mail.kmutt.ac.th (Poom Kumam) doi:10.22436/jmcs.017.01.03 Received 2016-02-10