The sections of odd univalent functions (Q799829)
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scientific article; zbMATH DE number 3873647
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The sections of odd univalent functions |
scientific article; zbMATH DE number 3873647 |
Statements
The sections of odd univalent functions (English)
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1984
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Let \(S_ 2\) be the class of functions \(f(z)=z+\sum^{\infty}_{n=1}b_ nz^{2n+1}\) regular and univalent in \(| z| <1\) and denote \(s_ n(z)=z+\sum^{n}_{k=1}b_ kz^{2k+1}.\) The authors prove that all the sections \(s_ n(z)\) are starlike in \(| z| <1/\sqrt{3}.\quad\rho_*=1/\sqrt{3}\) is best possible as shown by the function \(z/(1-z^ 2).\)
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starlike functions
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odd univalent functions
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