Convergence and numerical analysis of a family of two-step steffensenʹs methods

We provide sufficient conditions for the semilocal convergence of a family of two-step Steffensenʹs iterative methods on a Banach space. The main advantage of this family is that it does not need to evaluate neither any Fréchet derivative nor any bilinear operator, but having a high speed of convergence. Some numerical experiments are also presented.