Abstract
In this paper, we prove some unique common fixed point theorem for two pairs of weakly compatible mappings, satisfying the rational contraction conditions in complex valued metric space. The proved result, generalize and extend some known results in the literature. Finally, The main result is the application of the Urysohn integral equations to derive the existence theorem for a general solution. AMS(MOS) Subject Classification Codes: 47H10, 54H25.
Highlights
The theory of complex valued metric space (CV MS) is developed by A
He created unique common fixed point results for pair of compatible mappings satisfying a rational inequality
Very much inventor have established several results of fixed points for various mappings satisfying a rational contraction in the context of the complex valued metric spaces, see for [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]
Summary
The theory of complex valued metric space (CV MS) is developed by A. Imdad [3], which is a generalization of metric space. He created unique common fixed point results for pair of compatible mappings satisfying a rational inequality. Very much inventor have established several results of fixed points for various mappings satisfying a rational contraction in the context of the complex valued metric spaces, see for [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]. The purpose of this paper is to build up the common fixed point result for two sets of compatible mappings satisfying rational contraction in a complex valued metric space and we acquire the presence and uniqueness of a common solution for the arrangement of Urysohn integral equation
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