Approximating existence and uniqueness of solution for a nonlinear IVP of first order ordinary iterative differential equations

Approximating solutions of nonlinear iterative differential equations

Abstract

In this paper we prove approximation theorems for existence and uniqueness of solution of a nonlinear IVP of first order ordinary iterative differential equation. Our analysis makes use of Dhage
iteration method based on a Schauder type hybrid fixed point theorem due Dhage (2022) while establishing our results.
The algorithms have also been established for approximating the solution. Finally, an example is also
provided to illustrate the main existence result of this paper.