On the asymptotic Bieberbach conjecture

Mauriso Alves and Armando J. P. Cavalcante

International Journal of Mathematics and Mathematical Sciences, 1982, vol. 5, 1-7

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 N 0 such that, for any f ( z ) = z + ? n = 2 8 a n z n ? S with | a 3 | = 2.58 , we have | a n | < n for all n > N 0 .

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:581927

DOI: 10.1155/S0161171282000507

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