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.

Keywords

• Fixed points
• periodic points
• commuting functions minimal sets.