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Fekete-Szegő problem for starlike and convex functions of complex order. (English) Zbl 1189.30021
Summary: For a non-zero complex number \(b\), let \(\mathcal F_n (b)\) denote the class of normalized univalent functions \(f\) satisfying
\[ \text{Re\,}\left[1+\frac{1}{b}\left(\frac{z(D^nf)'(z)}{D^nf(z)}-1\right)\right]> 0 \] in the unit disk \(\mathcal U\), where \(D^{n}f\) denotes the Ruscheweyh derivative of \(f\). Sharp bounds for the Fekete-Szegö functional \(\big|a_3 - \mu a^2_2\big|\) are obtained.

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