On the convergence of a higher order family of methods and its dynamics

摘要

In this paper, we present the study of the local convergence of a higher-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials is studied. Some anomalies are found in this family by means of studying the associated rational function. Parameter spaces are shown and the study of the stability of all the fixed points is presented.