Distortion theorems for classes of univalent functions (Q2754521)
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scientific article; zbMATH DE number 1671247
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Distortion theorems for classes of univalent functions |
scientific article; zbMATH DE number 1671247 |
Statements
11 November 2001
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univalent function
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convex function
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distortion theorems
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Distortion theorems for classes of univalent functions (English)
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Some well known results on special classes functions are derived in the paper. For example [see \textit{G. Schober}, Univalent functions (1975; Zbl 0306.30018)] the \(n\)th derivative of convex function satisfies the following inequality NEWLINE\[NEWLINE|f^{(n)}(z)|\leq {n!\over (1-|z|)^{n+ 1}}NEWLINE\]NEWLINE for \(|z|< 1\), \(n= 2,3,\dots\)\ . In the case \(n=2\), the inequality is a main result of the paper.NEWLINENEWLINEFor the entire collection see [Zbl 0956.00027].
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