On certain sufficient conditions for starlikeness (Q1578351)
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scientific article; zbMATH DE number 1496718
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On certain sufficient conditions for starlikeness |
scientific article; zbMATH DE number 1496718 |
Statements
On certain sufficient conditions for starlikeness (English)
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8 February 2001
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The author makes use of the method of differential subordination due to S. Miller and P. T. Mocanu [Mich. Math. J. 28, 157-172 (1981; Zbl 0456.30022)] to obtain some sufficient conditions for starlikeness. A typical result is as follows: If \(f(z)=z+ \sum^\infty_{k=2} a_kz^k\) for \(|z|<1\) and \[ f(z)f''(z) \bigl(f'(z) \bigr)^{-2} \prec 2-2(1-z)^2 \] holds the unit disk, then \(f\) is starlike univalent.
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conditions for starlikeness
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