A family of Newton-type methods for solving nonlinear equations

A family of Newton-type methods free from second and higher order derivatives for solving nonlinear equations is presented. The order of the convergence of this family depends on a function. Under a condition on this function this family converge cubically and by imposing one condition more on this function one can obtain methods of order four. It has been shown that this family covers many of the available iterative methods. From this family two new iterative methods are obtained. Numerical experiments are also included.