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Fekete-Szegő functional for non-Bazilevič functions. (English) Zbl 1017.30012
Let \(0<\lambda <1\). The authors consider the class of holomorphic functions \(f(z)=z+a_2 z^2+\dots \) in the unit \(\mathcal U:=\{|z|<1\}\) with the property that \(f'(z)(z/f(z))^{1+\lambda}\) has positive real part for all \(z\in \mathcal U\). For those functions they give sharp estimates for \(|a_2|\) as well as for the Fekete–Szegö functional \(|a_3-\mu a^2_2|\), where \(\mu\) is an arbitrary complex number.

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