Third-order methods on Riemannian manifolds under Kantorovich conditions

One of the most studied problems in numerical analysis is the approximation of nonlinear equations using iterative methods. In the past years, attention has been paid in studying Newton's method on manifolds. In this paper, we generalize this study by considering a general class of third-order iterative methods. A characterization of the convergence under Kantorovich type conditions and optimal error estimates is found.