The order of convergence of some families of iterative methods for solving nonlinear equations

We focus on some families of iterative methods. A few particular cases of these families are: Newton's method, Halley's method, Euler's method, Osculating parabola method, Chebyshev's method and others. For each families we started with a definition, we continue with particular cases and examples. For each these families we get their convergence order. We also obtain for some polynomials the attraction basins of the studied methods.