Some Geraghty Type Inequalities in b-fuzzy Metric Spaces with an Application

In this note, we introduce novel Geraghty-type inequalities within the framework of a b-fuzzy metric space and develop new fixed point theorems for such mappings in a G-complete b-fuzzy metric space. To substantiate our findings, we present several illustrative examples using graphical methods. Additionally, we demonstrate the application of our introduced theorems by solving a non-linear integral equation, showing the practical utility of our results.