AUTHORS: Ioannis K. Argyros, Santhosh George

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ABSTRACT: The goal of this paper is to present a local convergence analysis of Newton’s method for approximating a locally unique solution of an equation in a Banach space setting. Using the gauge function theory and our new idea of restricted convergence regions we present an extended and unified convergence theory.

KEYWORDS: Newton’s method, Banach space, semilocal convergence, gauge function, convergence region, Newton-Kantorovich theorem

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