A semilocal convergence result for Newton’s method under generalized conditions of Kantorovich

From Kantorovich’s theory we establish a general semilocal convergence result for Newton’s method based fundamentally on a generalization required to the second derivative of the operator involved. As a consequence, we obtain a modification of the domain of starting points for Newton’s method and improve the a priori error estimates. Finally, we illustrate our study with an application to a special case of conservative problems.