On the Attainable Order of Convergence for Some Multipoint Iteration Functions

In this paper, we deal with a class of multipoint iterative formulas that find new approximations to a zero of a function f(x). First of all, we show that the attainable order of convergence is equal to 7 for a class of formulas that require two evaluations off(x) and two of f'(x) per iteration. Furthermore, we show that the attainable order of convergence is equal to 4 for a class of formulas that require one evaluation of f(x) and two of f'(x) per iteration and that the attainable order of convergence is equal to 4 for a class of formulas that require two evaluations of f(x) and one of f'(x) per iteration.