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Mat. Zametki, 1972, Volume 12, Issue 2, Pages 127–130 (Mi mz9858)  

A bound for the coefficient $c_4$ for one-sheeted functions in terms of $|c_2|$

V. A. Baranova

Leningrad State University

Abstract: In the class $S$ of functions $f(z)=z+\sum_{k=2}^\infty c_kz^k$ which are regular and single-sheeted in the circle $|z|<1$, the bound for $|c_4|$ in terms of $|c_2|$, obtained by Al'fors, is improved. The crudest bound $|c_4|\leqslant4/15(11+|c_2|)$ is better than that of Al'fors: $|c_4|\leqslant(4/\sqrt{15})\sqrt{11+|c_2|^2}$.

Full text: PDF file (350 kB)

English version:
Mathematical Notes, 1972, 12:2, 510–512

Bibliographic databases:

UDC: 517.5
Received: 18.10.1971

Citation: V. A. Baranova, “A bound for the coefficient $c_4$ for one-sheeted functions in terms of $|c_2|$”, Mat. Zametki, 12:2 (1972), 127–130; Math. Notes, 12:2 (1972), 510–512

Citation in format AMSBIB
\Bibitem{Bar72}
\by V.~A.~Baranova
\paper A bound for the coefficient $c_4$ for one-sheeted functions in terms of $|c_2|$
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 2
\pages 127--130
\mathnet{http://mi.mathnet.ru/mz9858}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=316698}
\zmath{https://zbmath.org/?q=an:0242.30012}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 2
\pages 510--512
\crossref{https://doi.org/10.1007/BF01095007}


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