An Intermediate Newton Iterative Scheme and Generalized Zabrejko-nguen and Kantorovich Existence Theorems for Nonlinear Equations

We revisit a one-step intermediate Newton iterative scheme that was used by Uko and Velásquez in [17] for the constructive solution of nonlinear equations of the type f(u) + g(u) = 0 . By utilizing weaker hypotheses of the Zabrejko-Nguen kind and a modified majorizing sequence we perform a semilocal convergence analysis which yields finer error bounds and more precise information on the location of the solution that the ones obtained in [17]. We also give two generalizations of the well-known Kantorovich theorem on the solvability of nonlinear equations and the convergence of Newton’s method. Illustrative examples are provided in the paper. MSC 2010. 65H99, 49M15.