C-class and F(ψ,φ)-contractions on M-metric spaces

Partial 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 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(ψ,ϕ)-contractions and investigate the existence and uniqueness of fixed points for the new classC 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.