Improved generalized differentiability conditions for Newton-like methods

We provide a semilocal convergence analysis for Newton-like methods using the ω$\omega$-versions of the famous Newton–Kantorovich theorem (Argyros (2004) 1], Argyros (2007) 3], Kantorovich and Akilov (1982) 13]). In the special case of Newton’s method, our results have the following advantages over the corresponding ones (Ezquerro and Hernaández (2002) 10], Proinov (2010) 17]) under the same information and computational cost: finer error estimates on the distances involved; at least as precise information on the location of the solution, and weaker sufficient convergence conditions.