Certain improvements of Chebyshev–Halley methods with accelerated fourth-order convergence

In this paper, we present a new one-parameter family of methods which improves the classical Chebyshev–Halley methods with cubic convergence. The convergence analysis shows that each method of the family is quartically convergent and per iteration it requires one evaluation of the given function and two of its first derivative. The well-known Jarratt fourth-order method is shown to be part of the family. Several numerical examples are given to illustrate the efficiency and performance of the presented methods.