International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 269-276
doi:10.1155/S0161171298000386

On common fixed and periodic points of commuting functions

Abstract

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.