On the convergence of an optimal fourth-order family of methods and its dynamics

In this paper, we present the study of the semilocal and local convergence of an optimal fourth-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 be means of studying the dynamical behavior. Parameter spaces are shown and the study of the stability of all the fixed points is presented.