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The Landau problem for bounded nonvanishing functions. (English) Zbl 0945.30011

The problem of finding: \[ L_n(B_0):=\sup|a_0+a_1+ \cdots+ a_n |, \quad n\geq 1, \] for the class \(B_0\) of holomorphic bounded and nonvanishing functions \(f(z)=a_0+ a_1z+ \dots\) in the unit disk \(|z|<1\) is discussed.

MSC:

30C50 Coefficient problems for univalent and multivalent functions of one complex variable
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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