Extending the applicability of Newton's method for k-Fréchet differentiable operators in Banach spaces

We extend the applicability of Newton's method for k-Fréchet differentiable operators in a Banach space setting by using a more flexible way of computing upper bounds on the inverses of the operators involved. In particular, we improve and extend the recent works by Ezquerro et al. (2012, 2013) [13,15]. Moreover, we illustrate our study with some numerical examples involving Hammerstein integral equations.