In this paper, we firstly introduce a new notion of inverse Ck-class functions which extends the notion of inverse C-class functions introduced by Saleem et al., 2018. Secondly, some common fixed point theorems are stated under some compatible conditions such as weak semicompatible of type A, weak semicompatibility, and conditional semicompatibility in metric spaces. Moreover, we introduce a new kind of compatibility called Sτ-compatibility which is weaker than E.A. property and also present a common fixed point theorem in metric spaces via inverse Ck-class functions. Some examples are provided to support our results.