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 Sibirsk. Mat. Zh.: Year: Volume: Issue: Page: Find

 Sibirsk. Mat. Zh., 2005, Volume 46, Number 6, Pages 1316–1323 (Mi smj1041)

Estimates for integral means of hyperbolically convex functions

I. R. Kayumov, Yu. V. Obnosov

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University

Abstract: We prove the Mejia–Pommerenke conjecture that the Taylor coefficients of hyperbolically convex functions in the disk behave like $O(\log^{-2}(n)/n)$ as $(n\to\infty)$ assuming that the image of the unit disk under such functions is a domain of bounded boundary rotation. Moreover, we obtain some asymptotically sharp estimates for the integral means of the derivatives of such functions and consider an example of a hyperbolically convex function that maps the unit disk onto a domain of infinite boundary rotation.

Keywords: conformal mapping, univalent function, hyperbolically convex function, integral means

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English version:
Siberian Mathematical Journal, 2005, 46:6, 1062–1068

Bibliographic databases:

UDC: 517.54
Revised: 24.06.2005

Citation: I. R. Kayumov, Yu. V. Obnosov, “Estimates for integral means of hyperbolically convex functions”, Sibirsk. Mat. Zh., 46:6 (2005), 1316–1323; Siberian Math. J., 46:6 (2005), 1062–1068

Citation in format AMSBIB
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\by I.~R.~Kayumov, Yu.~V.~Obnosov
\paper Estimates for integral means of hyperbolically convex functions
\jour Sibirsk. Mat. Zh.
\yr 2005
\vol 46
\issue 6
\pages 1316--1323
\mathnet{http://mi.mathnet.ru/smj1041}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2195031}
\zmath{https://zbmath.org/?q=an:1117.30010}
\transl
\jour Siberian Math. J.
\yr 2005
\vol 46
\issue 6
\pages 1062--1068
\crossref{https://doi.org/10.1007/s11202-005-0100-4}
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