Geodesic
Integral Estimates for the Derivatives of Univalent Functions
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 2, pp. 83-90

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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.
Mots-clés : Brennan's conjecture
Keywords: approximation by simple fractions. 
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     author = {F. D. Kayumov},
     title = {Integral {Estimates} for the {Derivatives} of {Univalent} {Functions}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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     publisher = {mathdoc},
     volume = {155},
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     url = {http://geodesic.mathdoc.fr/item/UZKU_2013_155_2_a6/}
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F. D. Kayumov. Integral Estimates for the Derivatives of Univalent Functions. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 2, pp. 83-90. http://geodesic.mathdoc.fr/item/UZKU_2013_155_2_a6/