The Carathéodory Inequality on the Boundary for Holomorphic Functions in the Unit Disc
In this paper, a boundary version of the Carathéodory inequality is studied. For the function f(z), defined in the unit disc with f(0) = 0, R f(z) ≤ A, we estimate a modulus of angular derivative at the boundary point z0, Rf(z0) = A, by taking into account the first two nonzero Maclaurin coefficient...
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| Дата: | 2016 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2016
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/140556 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Carathéodory Inequality on the Boundary for Holomorphic Functions in the Unit Disc / B.N. Örnek // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 4. — С. 287-301. — Бібліогр.: 9 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-140556 |
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dspace |
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irk-123456789-1405562018-07-11T01:23:12Z The Carathéodory Inequality on the Boundary for Holomorphic Functions in the Unit Disc Örnek, B.N. In this paper, a boundary version of the Carathéodory inequality is studied. For the function f(z), defined in the unit disc with f(0) = 0, R f(z) ≤ A, we estimate a modulus of angular derivative at the boundary point z0, Rf(z0) = A, by taking into account the first two nonzero Maclaurin coefficients. The sharpness of these estimates is also proved. 2016 Article The Carathéodory Inequality on the Boundary for Holomorphic Functions in the Unit Disc / B.N. Örnek // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 4. — С. 287-301. — Бібліогр.: 9 назв. — англ. 1812-9471 DOI : doi.org/10.15407/mag12.04.287 Mathematics Subject Classification 2000: 30C80 http://dspace.nbuv.gov.ua/handle/123456789/140556 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
In this paper, a boundary version of the Carathéodory inequality is studied. For the function f(z), defined in the unit disc with f(0) = 0, R f(z) ≤ A, we estimate a modulus of angular derivative at the boundary point z0, Rf(z0) = A, by taking into account the first two nonzero Maclaurin coefficients. The sharpness of these estimates is also proved. |
| format |
Article |
| author |
Örnek, B.N. |
| spellingShingle |
Örnek, B.N. The Carathéodory Inequality on the Boundary for Holomorphic Functions in the Unit Disc Журнал математической физики, анализа, геометрии |
| author_facet |
Örnek, B.N. |
| author_sort |
Örnek, B.N. |
| title |
The Carathéodory Inequality on the Boundary for Holomorphic Functions in the Unit Disc |
| title_short |
The Carathéodory Inequality on the Boundary for Holomorphic Functions in the Unit Disc |
| title_full |
The Carathéodory Inequality on the Boundary for Holomorphic Functions in the Unit Disc |
| title_fullStr |
The Carathéodory Inequality on the Boundary for Holomorphic Functions in the Unit Disc |
| title_full_unstemmed |
The Carathéodory Inequality on the Boundary for Holomorphic Functions in the Unit Disc |
| title_sort |
carathéodory inequality on the boundary for holomorphic functions in the unit disc |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/140556 |
| citation_txt |
The Carathéodory Inequality on the Boundary for Holomorphic Functions in the Unit Disc / B.N. Örnek // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 4. — С. 287-301. — Бібліогр.: 9 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
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