Fixed points of analytic complex functions on unit disk $\mathbb{D}$

Let $f: \mathbb{D}\rightarrow \mathbb{D}$ be an analytic complex valued function, where $\mathbb{D}$ is the unit disk. How many of fixed points  $f$ may have in $\mathbb{D}$ ?

Complex Analysis Functional Analysis Partial Differential Equations
Ering Ering
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Erdos Erdos
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