The improvements of Chebyshev–Halley methods with fifth-order convergence

In this paper, we present a family of new fifth-order methods, which improves the classical Chebyshev–Halley methods with cubic convergence. The new methods add one evaluation of the function at the point iterated by Chebyshev–Halley methods. Analysis of efficiency shows that the new methods can be of practical interest, which is also corroborated by numerical tests.