Some variants of King's fourth-order family of methods for nonlinear equations

In this paper, we present fourth-order families of new variants of King's fourth-order family of methods for solving nonlinear equations. Per iteration the obtained methods require two evaluations of the given function and one of its first derivative. The classical Traub-Ostrowski method is obtained as a special variant of King's method. Several numerical examples are given to illustrate the efficiency and performance of the presented methods.