Fixed point and periodic point results for α-type F-contractions in modular metric spaces

*Correspondence: [email protected] 1Theoretical and Computational Science Center (TaCS-Center), Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand 3Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan Full list of author information is available at the end of the article Abstract Motivated by Gopal et al. (Acta Math. Sci. 36B(3):1-14, 2016). We introduce the notion of α-type F-contraction in the setting of modular metric spaces which is independent from one given in (Hussain et al. in Fixed Point Theory Appl. 2015:158, 2015). Further, we establish some fixed point and periodic point results for such contraction. The obtained results encompass various generalizations of the Banach contraction principle and others.