Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228120170701$C$-class and $F(\psi,\varphi)$-contractions on $M$-metric spaces209224250210.22075/ijnaa.2017.1636.1429ENHosseinMonfaredDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranMahdiAzhiniDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranMehdiAsadiDepartment of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, IranJournal Article20160928Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In 2014 Asadi and {\it et al.} [New Extension of $p$-Metric Spaces with Some fixed point Results on $M$-metric paces, J. Ineq. Appl. 2014 (2014): 18] extend the Partial metric spaces to $M$-metric spaces. In this work, we introduce the class of $F(\psi,\varphi)$-contractions and investigate the existence and uniqueness of fixed points for the new class $\mathcal{C}$ in the setting of $M$-metric spaces. The theorems that we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions.https://ijnaa.semnan.ac.ir/article_2502_9859ace6f794b72f4e7dcfdcef8fbe62.pdf