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Coefficient inequality for a function whose derivative has a positive real part. (English) Zbl 1134.30310

Summary: Let \(\mathcal R\) denote the subclass of normalised analytic univalent functions \(f\) defined by \(f(z)=z+\sum^\infty_{n=2}a_nz^n\) which satisfy \[ \mathrm{Re}\{f'(z)\}>0 \] where \(z\in{\mathcal D}=\{z: |z|<1\}\). The object of the present paper is to introduce the functional \(|a_2a_4-a^2_3|\). For \(f\in\mathcal R\), we give sharp upper bound on \(|a_2a_4-a^2_3|\).

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
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