Improved generalized differentiability conditions for Newton-like methods

We provide a semilocal convergence analysis for Newton-like methods using the ωω-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.Numerical examples, involving a Chandrasekhar-type nonlinear integral equation as well as a differential equation with Green’s kernel are provided in this study.