A robust semi-local convergence analysis of Newton’s method for cone inclusion problems in Banach spaces under affine invariant majorant condition

A semi-local analysis of Newton’s method for solving nonlinear inclusion problems in Banach space is presented in this paper. Under an 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, our analysis retrieves the classical results on semi-local analysis of Newton’s method.