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 class 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.