On the asymptotic Bieberbach conjecture
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 fo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171282000507 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |