Some fixed point results for rational contraction on perturbed metric space

Abstract

This work is devoted to the study of fixed point theory for $F$-perturbed mappings in complete perturbed metric spaces. Specifically, we introduce the concept of rational type $F$-contraction and prove the existence and uniqueness of fixed points for such mappings. Our findings generalize several known results in the literature, extending the scope of the classical Banach contraction principle. The validity of the main results is demonstrated by means of an illustrative example.