A note on “New classes of iterative methods for nonlinear equations” and “Some iterative methods free from second derivatives for nonlinear equations”

In [M.A. Noor, New classes of iterative methods for nonlinear equations, Appl. Math. Comput., in press; M.A. Noor, Some iterative methods free from second derivatives for nonlinear equations, Appl. Math. Comput., in press], Noor introduced a generalized one parameter Halley’s methodxn+1=xn-f(xn)f′2(xn)f′3(xn)-αf(xn)f″(xn)for solving the nonlinear equation f(x) = 0. Noor further showed that for α=12f′(xn), the above method reduces to the Halley’s method [E. Halley, A new exact and easy method for finding the roots of equations generally and without any previous reduction, Philos. Roy. Soc. London 18 (1964) 136–147].It is interesting to note that for α=f′3(xn)f(xn)f′′(xn), the above method fails. In this note, we point out some major bugs in the results of Noor (in press).