  A semi-local analysis of Newton's method for solving nonlinear inclusion
problems in Banach space is presented in this paper. Under a affine majorant
condition on the nonlinear function which is associated to the inclusion
problem, the robust convergence of the method and results on the convergence
rate are established. Using this result we show that the robust analysis of the
Newton's method for solving nonlinear inclusion problems under affine
Lipschitz-like and affine Smale's conditions can be obtained as a special case
of the general theory. Besides for the degenerate cone, which the nonlinear
inclusion becomes a nonlinear equation, ours analysis retrieve the classical
results on local analysis of Newton's method.
