Geodesic
On the Univalence of Derivatives of Functions which are Univalent in Angular Domains
Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 885-890

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We consider functions $f$ that are univalent in a plane angular domain of angle $\alpha\pi$, $0<\alpha\le2$. It is proved that there exists a natural number $k$ depending only on $\alpha$ such that the $k$th derivatives $f^{(k)}$ of these functions cannot be univalent in this angle. We find the least of the possible values of for $k$. As a consequence, we obtain an answer to the question posed by Kiryatskii: if $f$ is univalent in the half-plane, then its fourth derivative cannot be univalent in this half-plane.
Keywords: univalent function, holomorphic function, Bieberbach's conjecture, Koebe function, Weierstrass theorem. 
S. R. Nasyrov. On the Univalence of Derivatives of Functions which are Univalent in Angular Domains. Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 885-890. http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a7/
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