Ball convergence of some fourth and sixth-order iterative methods (Q2805942)

This paper presents a local convergence analysis for a family of fourth and sixth-order iterative methods for approximating a locally unique solution of a nonlinear equation in a general Banach space. The main novelty of the analysis is that it requires only certain conditions on the first Fréchet derivative, instead of higher-order ones as often appeared in the existing literature. The convergence radius and error bounds are also given. The paper concludes with three brief numerical examples.