Orbital Contractions in JS-Metric Spaces with Directed Graphs and Applications to Nonlinear Integral Equations.

Source abstract

We establish new fixed point theorems for a novel class of contraction mappings in generalized metric spaces, commonly known as JS-metric spaces due to Jleli and Samet \cite{JS}, endowed with directed graphs. By introducing the concept of orbital contractions, we relax classical structural requirements and provide a necessary and sufficient condition for the existence of fixed points. Moreover, we provide an application to the existence of solutions for nonlinear integral equations to demonstrate the effectiveness of our main results.