Note on certain subclass of close-to-convex functions of order \(\alpha\) (Q916820)
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scientific article; zbMATH DE number 4154812
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Note on certain subclass of close-to-convex functions of order \(\alpha\) |
scientific article; zbMATH DE number 4154812 |
Statements
Note on certain subclass of close-to-convex functions of order \(\alpha\) (English)
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1990
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The authors prove: If f is holomorphic in the unit disk U, \(f(0)=f'(0)- 1=0\) and \[ | f'(z)-1| <1-\alpha \text{ for } z\in U \] then \[ Re e^{i\beta}f(z)/z<0\text{ for } | \beta | <(\pi /2)-\arcsin (1-\alpha) \] and \(z\in U\).
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