Common Fixed Point Theorems via Inverse C k − Class Functions in Metric Spaces

Abstract

In this paper, we firstly introduce a new notion of inverse $C_k-$ 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 $\left(A\right)$ , weak semicompatibility, and conditional semicompatibility in metric spaces. Moreover, we introduce a new kind of compatibility called $S_{\tau }-$ compatibility which is weaker than $\left(E.A.\right)$ property and also present a common fixed point theorem in metric spaces via inverse $C_k-$ class functions. Some examples are provided to support our results.