%0 Journal Article
%T Unified Local Convergence for Newton¡¯s Method and Uniqueness of the Solution of Equations under Generalized Conditions in a Banach Space
%J Mathematics | An Open Access Journal from MDPI
%D 2019
%R https://doi.org/10.3390/math7050463
%X Under the hypotheses that a function and its Fr¨¦chet derivative satisfy some generalized Newton¨CMysovskii conditions, precise estimates on the radii of the convergence balls of Newton¡¯s method, and of the uniqueness ball for the solution of the equations, are given for Banach space-valued operators. Some of the existing results are improved with the advantages of larger convergence region, tighter error estimates on the distances involved, and at-least-as-precise information on the location of the solution. These advantages are obtained using the same functions and Lipschitz constants as in earlier studies. Numerical examples are used to test the theoretical results. View Full-Tex
%U https://www.mdpi.com/2227-7390/7/5/463