Dhage iteration method in the theory of IVPs  of nonlinear first order  functional differential equations

Bapurao C. Dhage1*

doi:10.26637/MJM0504/0011

Dhage iteration method in the theory of IVPs of nonlinear first order functional differential equations

Authors :

Bapurao C. Dhage^1*

Author Address :

¹Kasubai, Gurukul Colony, Thodga Road, Ahmedpur-413515, Dist. Latur, Maharashtra, India.

*Corresponding author.

Abstract :

In this paper we discuss a couple of nonlinear hybrid functional differential equations involving a delay and explain the power of a new iteration method in applications. In particular, we prove the existence and uniqueness results for approximate solutions of an initial value problem of first order nonlinear hybrid functional differential equation via construction of an algorithm. The main results rely on the Dhage iteration method embodied in a recent hybrid fixed point principle of Dhage (2014) in a partially ordered normed linear space. Examples are also furnished to illustrate the hypotheses and the abstract results of this paper.

Keywords :

Hybrid functional differential equation; Hybrid fixed point principle; Dhage iteration method; Existence and approximation theorem.

DOI :

10.26637/MJM0504/0011

Article Info :

Received : July 08, 2017; Accepted : September 03, 2017.