Some variants of Chebyshev-Halley methods with fifth-order convergence

In this paper, we present some new variants of Chebyshev-Halley methods. The local order of convergence is increased from 3 to 5. The new methods add one evaluation of the function at the point iterated by Chebyshev-Halley methods. The numerical results show that the new methods work better not only in order but in efficiency.