On common fixed and periodic points of commuting functions

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

A counter example on common periodic points of functions

By a counter example we show that two continuous functions defined on a compact metric space satisfying a certain semi metric need not have a common periodic point

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

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

On common fixed points, periodic points, and recurrent points of continuous functions

It is known that two commuting continuous functions on an interval need not have a common fixed point. However, it is not known if such two functions have a common periodic point. we had conjectured that two commuting continuous functions on an interval will typically have disjoint sets of periodic points. In this paper, we first prove that S is a nowhere dense subset of [0,1] if and only if {f∈C([0,1]):Fm(f)∩S¯≠∅} is a nowhere dense subset of C([0,1]). We also give some results about the common fixed, periodic, and recurrent points of functions. We consider the class of functions f with continuous ωf studied by Bruckner and Ceder and show that the set of recurrent points of such functions are closed intervals

© Hindawi Publishing Corp. ON COMMON FIXED POINTS, PERIODIC POINTS, AND RECURRENT POINTS OF CONTINUOUS FUNCTIONS

It is known that two commuting continuous functions on an interval need not have a common fixed point. However, it is not known if such two functions have a common periodic point. We had conjectured that two commuting continuous functions on an interval will typically have disjoint sets of periodic points. In this paper, we first prove that S is a nowhere dense subset of [0,1] if and only if {f ∈ C([0,1]) : Fm(f)∩S =∅}is a nowhere dense subset of C([0,1]).Wealsogive some results about the common fixed, periodic, and recurrent points of functions. We consider the class of functions f with continuous ωf studied by Bruckner and Ceder and show that the set of recurrent points of such functions are closed intervals