Fixed-Point Results for Generalized Rational Contractions in Graphical b-Metric Spaces with Applications

Abstract

The aim of this paper is to define generalized rational contractions in the setting of graphical $b$ -metric spaces and obtain some fixed-point theorems. Our results are significant generalizations and extensions of some well-known results in the existing theory. We also supply a nontrivial example to show the validity of the obtained theorems. As applications, we obtain some results on rational expressions in the background of graphical metric spaces.