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...
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| Format: | Article |
| Language: | English |
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Wiley
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171282000507 |
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| _version_ | 1832556294949568512 |
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| author | Mauriso Alves Armando J. P. Cavalcante |
| author_facet | Mauriso Alves Armando J. P. Cavalcante |
| author_sort | Mauriso Alves |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c10e70a9d079458b88017ffc08547a42 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1982-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c10e70a9d079458b88017ffc08547a422025-02-03T05:45:53ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251982-01-015353754310.1155/S0161171282000507On the asymptotic Bieberbach conjectureMauriso Alves0Armando J. P. Cavalcante1Department of Mathematics, Universidade Federal de Pernambuco, Recife, Pe 50.000, BrazilDepartment of Mathematics, Universidade Federal de Pernambuco, Recife, Pe 50.000, BrazilThe 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.http://dx.doi.org/10.1155/S0161171282000507univalent functions. |
| spellingShingle | Mauriso Alves Armando J. P. Cavalcante On the asymptotic Bieberbach conjecture International Journal of Mathematics and Mathematical Sciences univalent functions. |
| title | On the asymptotic Bieberbach conjecture |
| title_full | On the asymptotic Bieberbach conjecture |
| title_fullStr | On the asymptotic Bieberbach conjecture |
| title_full_unstemmed | On the asymptotic Bieberbach conjecture |
| title_short | On the asymptotic Bieberbach conjecture |
| title_sort | on the asymptotic bieberbach conjecture |
| topic | univalent functions. |
| url | http://dx.doi.org/10.1155/S0161171282000507 |
| work_keys_str_mv | AT maurisoalves ontheasymptoticbieberbachconjecture AT armandojpcavalcante ontheasymptoticbieberbachconjecture |