On the Fekete-Szegö problem for a class of analytic functions. (English) Zbl 1286.30015

Peng, Zhigang

ISRN Math. Anal. 2014, Article ID 861671, 4 p. (2014).

Summary: Let \(\mathcal A\) denote the class of functions which are analytic in the unit disk \(D=\{z:|z|<1\}\) and given by the power series \(f(z)=z+\sum^\infty_{n=2}a_nz^n\). Let \(C\) be the class of convex functions. In this paper, we give the upper bounds of \(|a_3-\mu a^2_2|\) for all real number \(\mu\) and for any \(f(z)\) in the family \(\mathcal V=\{f(z):f \in \mathcal A, \mathrm{Re}(f(z)/g(z))>0 \text{ for some } g\in C\}\).

MSC:

30C45

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

References:

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