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A semi-local analysis of Newton's method for solving nonlinear inclusionproblems in Banach space is presented in this paper. Under a affine majorantcondition on the nonlinear function which is associated to the inclusionproblem, the robust convergence of the method and results on the convergencerate are established. Using this result we show that the robust analysis of theNewton's method for solving nonlinear inclusion problems under affineLipschitz-like and affine Smale's conditions can be obtained as a special caseof the general theory. Besides for the degenerate cone, which the nonlinearinclusion becomes a nonlinear equation, ours analysis retrieve the classicalresults on local analysis of Newton's method.

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