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On the asymptotic Bieberbach conjecture

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  • Mauriso Alves
  • Armando J. P. Cavalcante

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 .

Suggested Citation

  • Mauriso Alves & Armando J. P. Cavalcante, 1982. "On the asymptotic Bieberbach conjecture," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 5, pages 1-7, January.
    • Handle: RePEc:hin:jijmms:581927
    DOI: 10.1155/S0161171282000507
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