An Approach of Integral Equations in Complex-Valued b -Metric Space Using Commuting Self-Maps

Abstract

This paper is aimed at establishing some unique common fixed point theorems in complex-valued $b$ -metric space under the rational type contraction conditions for three self-mappings in which the one self-map is continuous. A continuous self-map is commutable with the other two self-mappings. Our results are verified by some suitable examples. Ultimately, our results have been utilized to prove the existing solution to the two Urysohn integral type equations. This application illustrates how complex-valued $b$ -metric space can be used in other types of integral operators.