Existence of fixed points for a pair of mappings in complex valued metric space and application to integral equations

Abstract

In this paper, some sufficient conditions for the existence of common fixed points for two mappings in the setting of $C$-complex valued metric space are provided. Also, common fixed point theorems for weakly compatible mappings, weakly compatible mappings along with E.A and CLR properties have been established. Furthermore, as an application of the proved result, a solution to the integral equations of Urysohns' type has been obtained.