International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1982 / Article

Open Access

Volume 5 |Article ID 581927 | https://doi.org/10.1155/S0161171282000507

Mauriso Alves, Armando J. P. Cavalcante, "On the asymptotic Bieberbach conjecture", International Journal of Mathematics and Mathematical Sciences, vol. 5, Article ID 581927, 7 pages, 1982. https://doi.org/10.1155/S0161171282000507

On the asymptotic Bieberbach conjecture

Received11 Dec 1981

Abstract

The set S consists of complex functions f, univalent in the open unit disk, with f(0)=f'(0)-1=0. We use the asymptotic behavior of the positive semidefinite FitzGerald matrix to show that there is an absolute constant N0 such that, for any f(z)=z+?n=28anzn?S with |a3|=2.58, we have |an|<n for all n>N0.

Copyright © 1982 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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