Weak ψ-Contractions on Directed Graphs with Applications to Integral Equations

Abstract

This article deals with a few outcomes ensuring the fixed points of a weak $(G,\psi )$-contraction map of metric spaces comprised with a reflexive and transitive digraph G. To validate our findings, we furnish several examples. The findings we obtain enable us to seek out the unique solution of a nonlinear integral equation. The outcomes presented herewith sharpen, subsume, unify, improve, enrich, and compile a number of existing theorems.