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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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/140556 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862597634640838656 |
|---|---|
| author | Örnek, B.N. |
| author_facet | Örnek, B.N. |
| 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. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| 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.
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| first_indexed | 2025-11-27T18:43:38Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-140556 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-11-27T18:43:38Z |
| publishDate | 2016 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Örnek, B.N. 2018-07-10T16:09:11Z 2018-07-10T16:09:11Z 2016 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 https://nasplib.isofts.kiev.ua/handle/123456789/140556 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. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии The Carathéodory Inequality on the Boundary for Holomorphic Functions in the Unit Disc Article published earlier |
| spellingShingle | The Carathéodory Inequality on the Boundary for Holomorphic Functions in the Unit Disc Örnek, B.N. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/140556 |
| work_keys_str_mv | AT ornekbn thecaratheodoryinequalityontheboundaryforholomorphicfunctionsintheunitdisc AT ornekbn caratheodoryinequalityontheboundaryforholomorphicfunctionsintheunitdisc |