Statement
Let f be a holomorphic function in the unit disk |z| ≤ 1. Suppose that |f′(0)| = 1. Then there exists a disc of radius b and an analytic function φ in this disc, such that f(φ(z)) = z for all z in this disc. Here b > 1/72 is an absolute constant.
Read more about this topic: Bloch's Theorem (complex Variables)
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