International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 269-276

On common fixed and periodic points of commuting functions

Aliasghar Alikhani-Koopaei

Mathematics Department, University of Isfahan, Isfahan, Iran

Received 8 March 1996; Revised 30 March 1996

Copyright © 1998 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.


It is known that two commuting continuous functions on an interval need not have a common fixed point. It is not known if such two functions have a common periodic point. In this paper we first give some results in this direction. We then define a new contractive condition, under which two continuous functions must have a unique common fixed point.