Study of a biparametric family of iterative methods (Q1722172)

Summary: The dynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. This biparametric family includes the \(c\)-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 \((\alpha, c)\) with clear stable and unstable behaviors.