Geraghty type contractions in fuzzy $b$-metric spaces with application to integral equations

Abstract

In this paper, we study the notion of a fuzzy $b$-metric space and establish certain fixed point results for Geraghty-type contraction in the setting of $G$-complete fuzzy $b$-metric space. We furnish an example to illustrate our main result. Our results extend and generalize the existing results in the literature. An application related to our main result for the existence of solution of nonlinear integral equations is also presented.