Dynamical behaviors of some iterative methods for multiple roots of nonlinear equations

Recently, more and more higher-order iterative methods for finding the multiple roots of nonlinear equations have been presented. Most of them require the information of the multiplicity of roots. In this paper, the conjugacy maps and the extraneous fixed points of some iterative methods for finding the multiple roots are discussed, basins of attractions of them are also given to demonstrate their dynamical behaviors around the multiple roots for several polynomials.