Dhage iteration method for approximating positive solutions of quadratic functional differential equations

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Authors :

Bapurao C. Dhage1

Author Address :

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

Abstract :

In this paper we prove the existence and approximation theorems for positive solutions of a couple of nonlinear first order quadratic hybrid functional differential equations with delay under certain mixed conditions of algebra, geometry and topology. We employ the Dhage iteration method embodied in a hybrid fixed point principle of Dhage (2014) involving the product of two operators in a partially ordered Banach algebra in the discussion. A couple of numerical examples are also provided to indicate the applicability of the abstract results to some concrete problems of quadratic functional differential equations.

Keywords :

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



Article Info :

Received : October 12, 2017; Accepted : December 22, 2017.



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