Abstract
In this paper, a theorem for local existence of a unique solution for a system of nonlinear ordinary differential equations ( NODE ) of order m has been stated and proved. The proof was done using contractive mapping theorem in a metric space subset of the Banach space consisting of the bounded differentiable functions on the real numbers and equipped with a Bielescki's type norm. As an application of the theory, an example has been given.
 Index Terms : Banach space of bounded functions, Bielescki's type norm, Existence of a unique solution globally, System of nonlinear ordinary differential equations of order m.
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