A NECESSARY AND SUFFICIENT CONDITION FOR Q(f)=P(f) OF f∈C^0(I, I)

Denote C0（I, I） as the set of all continuous mappings of the interval. Let f∈C0（I, I）, for any positive integer n, we define fn inductively byf1= f, fn=f·fn-1 and f0=the identity map.Definition 1. Let p∈I. If. there exists a positive integer n, such that fn（p）=p, then p is called a periodic point of f.