On the speed of convergence of iteration of a function - Vladimir Drobot (International Journal of Mathematics and Mathematical Sciences)
Let fn(x) be the nth iterate of a function in some interval [0,c]. It is known that if f(x)∼x−xα, α>1, then fn(x)∼Ana for some A and a. In this paper we prove a converse of this theorem: The rate of convergence of the iterates determines the form of a function.