Fixed point results via O-$F_{\varrho}$ contraction and applications to Fredholm and integro-differential equations

Abstract

In this article, we introduce the new concept of an $O$-$\mathnormal{F}_{\varrho}$ contraction on $O$-controlled $O$-$b$-Branciari metric type spaces. We furnish the validity of our findings with appropriate examples. This approach is completely new and will be beneficial for the future aspects of the related study. We provide some applications of Fredholm integral equation and an integro-differential equation to illustrate the usability of our theory.