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Brief communications

Univalent functions without common values

D. A. Kirillova

Chair of Higher Mathematics, Far Eastern Academy for Humanities and Social Studies, Birobidzhan, Russia

Abstract: In this paper we establish inequalities involving moduli of derivatives $|f_k'(0)|$ of functions $f_k$ univalent in the unit disk $|z|<1$ having no common values and translating zero in a point on the segment $[-1,1]$, $k=1,\dots,n$. We estimate $f_k$ by means of Schwarzian derivatives.

Keywords: univalent functions, extremal partitions, conformal radius, Schwarzian derivative.

UDC: 517.54

Received: 29.01.2010

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:9, 74–76

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