International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 929475, 5 pages
Research Article

On the Set of Fixed Points and Periodic Points of Continuously Differentiable Functions

Department of Mathematics, Berks College, Pennsylvania State University, Tulpehocken Road, P.O. Box 7009, Reading, PA 19610-6009, USA

Received 6 December 2012; Accepted 16 February 2013

Academic Editor: Paolo Ricci

Copyright © 2013 Aliasghar Alikhani-Koopaei. 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.


In recent years, researchers have studied the size of different sets related to the dynamics of self-maps of an interval. In this note we investigate the sets of fixed points and periodic points of continuously differentiable functions and show that typically such functions have a finite set of fixed points and a countable set of periodic points.