Abstract

In this paper, we prove a couple of approximation results for local existence and uniqueness of the solution of an initial value problem of nonlinear first order ordinary hybrid differential equations with maxima under weaker partial compactness and partial Lipschitz type conditions using the Dhage monotone iteration method based on the recent hybrid fixed point theorems of Dhage. An approximation result for the Ulam-Hyers stability of the local solution of the considered hybrid differential equation with maxima is also established. Our main abstract results are also illustrated with a couple of numerical examples.

Keywords and Phrases

Initial value problem, Hybrid fixed point principle, Dhage monotone iteration method, Approximation result, Ulam-Hyers stability.

A.M.S. subject classification

34A12, 34A34, 34A45, 47H10.

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