Abstract
A new global Kantorovich-type convergence theorem for Newton's method in Banach space is provided for approximating a solution of a nonlinear equation. It is assumed that a solution exists and the second Fréchet-derivative of the operator involved satisfies a Lipschitz condition. Our convergence condition differs from earlier ones, and therefore it has theoretical and practical value. Finally, a simple numerical example is provided to show that our results apply, where earlier ones fail.
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