Radius problems for a subclass of close-to-convex univalent functions (Q1205611)
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scientific article; zbMATH DE number 147578
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Radius problems for a subclass of close-to-convex univalent functions |
scientific article; zbMATH DE number 147578 |
Statements
Radius problems for a subclass of close-to-convex univalent functions (English)
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1 April 1993
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Let \(f\) and \(F\) be analytic in the unit disc. Then \(f\) is said to be in \(P[A,B]\) if \(f\) is subordinate to \((1+Az)/(1+Bz)\) where \(-1\leq B<A\leq 1\). Further, for \(0\leq\beta<1\), \(F\) is in \(K_ \beta^*[A,B]\) if there is a function \(g\) with \(zg'(z)/g(z)\) in \(P[A,B]\) such that \({\mathcal R}(zF'(z))'/g(z)>\beta\). These classes are related to other classes of univalent functions.
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convex
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close-to-convex
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subordinate
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0.9532894
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0.94711787
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0.94009984
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