Dynamics of a multipoint variant of Chebyshev–Halley’s family

In this paper, a complex dynamical study of a parametric Chebyshev–Halley type family of iterative methods on quadratic polynomial is presented. The stability of the fixed points is analyzed in terms of the parameter of the family. We also calculate the critical points building their corresponding parameter planes which allow us to analyze the qualitative behavior of this family. Moreover, we locate some dynamical planes showing different pathological aspects of this family.