Relaxing Convergence Conditions for Newton’s Method1

The classical Kantorovich theorem on Newton’s method assumes that the first derivative of the operator involved satisfies a Lipschitz condition 0 F Žx. F Žy. L x y . In this paper, we weaken this condition, assuming that 0 F Žx. F Žx0. Ž x x0 . for a given point x0.