On common fixed point via inverse $C_{k}$-class functions in partially E-cone metric spaces

Abstract In this paper, we introduce common fixed point theorems through the context of inverse $C_{k}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:math> -class functions on partially E -cone metric spaces. We extend the existing fixed point theorem and explore the existence and uniqueness of common fixed point theorem under some compatible conditions such as semi-compatibility, semi-compatibility of type (A), weak semi-compatibility, conditional semi-compatibility and Sτ –compatibility. Examples are given to bolster our findings.