International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 3, Pages 537-543
doi:10.1155/S0161171282000507
On the asymptotic Bieberbach conjecture
Mauriso Alves
and Armando J.P. Cavalcante
Department of Mathematics, Universidade Federal de Pernambuco, Recife 50.000, Pe, Brazil
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=2∞anzn∈S with |a3|≤2.58, we have |an|<n for all n>N0.