On the Convergence of a Modified Newton Method for Solving Equations

We approximate a solution of a nonlinear operator equation in a Banach space setting, where the differentiability of the operator involved is not assumed using a modified Newton method considered also in [1], [2], [6], [11]-[15]. We provide new sufficient convergence conditions, which are weaker than before [1], [2], [6], [11]-[15], under the same computational cost. Numerical examples where our results apply, where earlier ones fail are also provided in this study.