On a new multiparametric family of Newton-like methods

Abstract

The main subject of this paper is the characterization of a modified family of Newton-type iterative processes of R-order at least three to approximate a solution of a nonlinear equation in Banach spaces. We weaken the usual semilocal convergence conditions, for this type of iterative processes, assuming that the second derivative is ω-conditioned. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)