The Fekete-Szegő problem for strongly close-to-convex functions

Abdel-Gawad, H. R.; Thomas, D. K.

doi:10.1090/S0002-9939-1992-1065939-0

The Fekete-Szegő problem for strongly close-to-convex functions
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by H. R. Abdel-Gawad and D. K. Thomas PDF

Proc. Amer. Math. Soc. 114 (1992), 345-349 Request permission

Abstract:

Let $K(\beta )$ denote the class of normalized analytic strongly close-to-convex functions of order $\beta \geq 0$, defined in the unit disc $D$ and let $f \in K(\beta )$, with $f(z) = z + {a_2}{z^2} + {a_3}{z^3} + \cdots$, for $z \in D$. Sharp bounds are obtained for $|{a_3} - \mu a_2^2|$ when $\mu$ is real.

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Eine Bermerkung über ungerade schlichte Funktionen

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