The Newton–Kantorovich hypothesis (15) has been used for a long time as a sufficient condition for convergence of Newton’s method to a locally unique solution of a nonlinear equation in a Banach… (More)

We extend the applicability of the Gauss–Newton method for solving singular systems of equations under the notions of average Lipschitz–type conditions introduced recently in Li et al. (J Complex… (More)

We present new sufficient conditions for the semilocal convergence of Newton’s method to a locally unique solution of an equation in a Banach space setting. Upper bounds on the limit points of… (More)

We provide a semilocal convergence analysis for Newton-like methods using the ω-versions of the famous Newton–Kantorovich theorem (Argyros (2004) [1], Argyros (2007) [3], Kantorovich and Akilov… (More)

A semilocal convergence analysis for directional two-step Newton methods in a Hilbert space setting is provided in this study. Two different techniques are used to generate the sufficient convergence… (More)