On rediscovered iteration methods for solving equations

In the recent papers of Gerlach (SIAM Rev. 36 (1994) 272–276) and Ford and Pennline (SIAM Rev. 38 (1996) 658–659) a class of iterative methods for solving a single equation f(x)=0, with arbitrary rate of convergence, has been presented. In this paper we show that this class is equivalent to five other classes of iterative methods, derived earlier in various ways and expressed in different forms. The proofs of equivalence of all considered iteration formulas are given.