Extended Newton's method for solving generalized equations under Kantorovich's-type weak conditions

The Kantorovich's methodology has been applied extensively to solve generalized equations using Newton's method. However, the mostly sufficient conditions limit the applicability of this method. But the method may converge even if these conditions are not satisfied. Therefore, it is important to show convergence to a solution under weaker conditions, and if possible without additional conditions. Motivated by optimization considerations and using more precise majorizing sequences we obtain the following advantages over either studies: Semi-Local Case: Extended convergence domain under the same or weaker convergence conditions, and tighter error bounds on the distances involved. Local Case: Enlarged radius of convergence and a finer error analysis. Our approach provides the same advantages in the case of Smale's theory for generalized equations.