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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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