A Kantorovich-type convergence analysis of Ulm's method [15] for solving smooth operator equations in Banach spaces is carried out assuming only regular smoothness of the operator involved instead of the usual Lipschitz smoothness. The theorem proved provides convergence condition, existence and uniqueness radii, a priori and a posteriori error bounds, which are shown to be sharp in the sense of [6]. The method is applied to Chandrasekhar's integral equation arising in radiative transfer.