Abstract:
In this paper, we prove Brennan's conjecture for conformal mappings $f$ of the disk $\{z:|z|<1\}$ assuming that the Taylor coefficients of the function $\log(zf'(z)/f(z))$ at zero are nonnegative. We also obtain inequalities for the integral means over the circle $|z|=r$ of the squared modulus of the function $zf'(z)/f(z)$.
Citation:
I. R. Kayumov, “On Brennan's Conjecture for a Special Class of Functions”, Mat. Zametki, 78:4 (2005), 537–541; Math. Notes, 78:4 (2005), 498–502
\Bibitem{Kay05}
\by I.~R.~Kayumov
\paper On Brennan's Conjecture for a Special Class of Functions
\jour Mat. Zametki
\yr 2005
\vol 78
\issue 4
\pages 537--541
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\zmath{https://zbmath.org/?q=an:1105.30009}
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\transl
\jour Math. Notes
\yr 2005
\vol 78
\issue 4
\pages 498--502
\crossref{https://doi.org/10.1007/s11006-005-0149-1}
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Linking options:
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https://doi.org/10.4213/mzm2612
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