Third-order iterative methods under Kantorovich conditions

We study a class of third-order iterative methods for nonlinear equations on Banach spaces. A characterization of the convergence under Kantorovich type conditions and optimal estimates of the error are found. Though, in general, these methods are not very extended due to their computational costs, we will show some examples in which they are competitive and even cheaper than other simpler methods. We center our analysis in both, analytic and computational, aspects.