A UNIFYING SEMILOCAL CONVERGENCE ANALYSIS FOR NEWTON-LIKE METHODS UNDER WEAK AND GATEAUX DIFFERENTIABILITY CONDITIONS

Abstract

We present sucient convergence conditions for the semilocal convergence of
Newton-like methods in order to approximate a locally unique solution of a nonlinear equation
containing a nondifferentiable term in a Banach space setting. The operators involved
are Fr{\'e}chet or Gateaux dierentiable. Our results unify, improve the error bounds and also
extend the applicability of earlier results. Numerical examples are also provided in this
study.