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International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 3, Pages 537-543
http://dx.doi.org/10.1155/S0161171282000507

On the asymptotic Bieberbach conjecture

Department of Mathematics, Universidade Federal de Pernambuco, Recife, Pe 50.000, Brazil

Received 11 December 1981

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.

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.