Hello this problem it´s looks easy, but I can´t do it. If you can give me some hint to do it )= It´s says this Let $f:\left[ {a,b} \right] \to \left[ {a,b} \right]$ be $C^1$. Let $p$ a fixed point of $f$ such that | f´(p) | < 1 Prove that there exist $\delta >0$ such that for every $x \in \left( {p - \delta ,p + \delta } \right)\Rightarrow \,\mathop {\lim }\limits_{n \to \infty } f^n \left( x \right) = p$.
Where $f^n \left( x \right)$ denotes the composite of functions , $n$ times