Study of a Biparametric Family of Iterative Methods

Thedynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. This biparametric family includes the ������-iterative methods and the well-known Chebyshev-Halley family.We find the analytical expressions for the fixed and critical points by solving 6-degree polynomials.We use the free critical points to get the parameter planes and, by observing them, we specify some values of (������, ������) with clear stable and unstable behaviors