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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2013, Volume 155, Book 2, Pages 83–90 (Mi uzku1208)  

This article is cited in 1 scientific paper (total in 1 paper)

Integral Estimates for the Derivatives of Univalent Functions

F. D. Kayumov

Kazan (Volga Region) Federal University

Abstract: In this paper we prove Brennans's conjecture for the conformal mapping of the unit circle on the assumption that even the Taylor coefficients of the function $\ln f'$ satisfies a certain condition. We also prove Brennan's conjecture for the case when there is an expansion of the function $1/f'$ into a series of simple fractions, provided that this series converges absolutely to zero. In addition, we obtain an estimate for the approximation of the function $1/f'$ by simple fractions.

Keywords: Brennan's conjecture, approximation by simple fractions.

Full text: PDF file (251 kB)
References: PDF file   HTML file
UDC: 517.54
Received: 25.01.2013

Citation: F. D. Kayumov, “Integral Estimates for the Derivatives of Univalent Functions”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 155, no. 2, Kazan University, Kazan, 2013, 83–90

Citation in format AMSBIB
\Bibitem{Kay13}
\by F.~D.~Kayumov
\paper Integral Estimates for the Derivatives of Univalent Functions
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2013
\vol 155
\issue 2
\pages 83--90
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1208}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. R. Kayumov, “Obzor po otsenkam spektra integralnykh srednikh konformnykh otobrazhenii”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2015, 104–115  mathnet  elib
  • Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
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