Argyros, I.K.George, S.2020-03-312020-03-312017WSEAS Transactions on Mathematics, 2017, Vol.16, , pp.248-256https://idr.nitk.ac.in/handle/123456789/11222The 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.Article