On Common Fixed Point Results for Integral Type Contractive Conditions in \(\varOmega \) -Metric Spaces and Application to Integral Equations

Sedghi and Dung (Fixed point theorems on \(\varOmega \) -metric spaces, 66(1) (2014), 113–124) demonstrated that \(d(\vartheta , \varkappa ) = \varOmega (\vartheta , \vartheta , \varkappa )\) may be used to derive the results of d-metric spaces from \(\varOmega \) -metric spaces. In this study, no ideas that correspond to the results of metric spaces are explored. In the framework of complete \(\varOmega \) -metric spaces, we construct standard fixed point theorems for integral type contractions involving rational terms and analyse their ramifications. In addition, we provide an example to support the outcome. Our findings extend and generalise a number of previously released findings. Finally, an application of the Fredhlom integral equation is discussed.