Fixed Point Theorem Apply to Modified Lipschitzcondition to Solve Differential Equations

Abstract

The goal of this work is to look at generalised contractions and show that they may be used to derive fixed point theorems in generalised metric spaces. Furthermore, we’ll also use fixed point theorems to show that the outcome of the ordinary differential equation exists and is exclusive (ODE). Fixed point theorem applies to modified Lipschitz condition. First, we have proved that generalised condition of Boyd Wong theorem and using this concept we have modified Lipschitz condition by adding constant which is suitable for solving differential equation.