International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 1, Pages 31-36

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

Received 13 May 1992; Revised 6 January 1993

Copyright © 1994 Vladimir Drobot. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let fn(x) be the nth iterate of a function in some interval [0,c]. It is known that if f(x)xxα, 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.