The Newtonian Operator and Global Convergence Balls for Newton’s Method - José A. Ezquerro; Miguel A. Hernández-Verón (Mathematics, 2020)
We obtain results of restricted global convergence for Newton’s method from ideas based on the Fixed-Point theorem and using the Newtonian operator and auxiliary points. The results are illustrated with a non-linear integral equation of Davis-type and improve the results previously given by the authors.