International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 1, Pages 31-36
doi:10.1155/S0161171294000050
On the speed of convergence of iteration of a function
Vladimir Drobot
Department of Mathematics and Computer Science, San Jose State University, San Jose 95192, CA, USA
Abstract
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.