Approximation results for PBVPs of nonlinear first order ordinary functional differential equations in a closed subset of the Banach space

Abstract

In this paper we prove the approximation results for existence and uniqueness of the solution of PBVPs of nonlinear first order ordinary functional differential equations in a closed subset of the Banach space. We employ the Dhage monotone iteration method based on a recent hybrid fixed point theorem of Dhage (2022) and Dhage {\em et al.} (2022) for the main results of this paper. Finally an example is indicated to illustrate the abstract ideas involed in the approximation results.