Norm estimation for pre-Schwarzian and Schwarzian derivatives of some univalent functions
UDC 517.5 Our purpose is to obtain estimates for the norms of Schwarzian and pre-Schwarzian derivatives of strongly starlike functions and strongly convex functions of order $\alpha$ and type $\beta.$ In addition, we present an example of a function $f \in S^*(\alpha, \beta)$ that cannot be $k$-q...
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| Дата: | 2026 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/8599 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513191558119424 |
|---|---|
| author | Wu, Xiaobin Zhu, Wanghao Wu, Xiaobin Zhu, Wanghao |
| author_facet | Wu, Xiaobin Zhu, Wanghao Wu, Xiaobin Zhu, Wanghao |
| author_sort | Wu, Xiaobin |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:39:38Z |
| description | UDC 517.5
Our purpose is to obtain estimates for the norms of Schwarzian and pre-Schwarzian derivatives of strongly starlike functions and strongly convex functions of order $\alpha$ and type $\beta.$ In addition, we present an example of a function $f \in S^*(\alpha, \beta)$ that cannot be $k$-quasiconformally extended for any $k < \alpha(1 - \beta).$ |
| doi_str_mv | 10.3842/umzh.v77i6.8599 |
| first_indexed | 2026-03-24T03:40:45Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8599 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:40:45Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-85992026-03-21T13:39:38Z Norm estimation for pre-Schwarzian and Schwarzian derivatives of some univalent functions Norm estimation for pre-Schwarzian and Schwarzian derivatives of some univalent functions Wu, Xiaobin Zhu, Wanghao Wu, Xiaobin Zhu, Wanghao pre-Schwarzian derivative Schwarzian derivative starlike functions convex functions UDC 517.5 Our purpose is to obtain estimates for the norms of Schwarzian and pre-Schwarzian derivatives of strongly starlike functions and strongly convex functions of order $\alpha$ and type $\beta.$ In addition, we present an example of a function $f \in S^*(\alpha, \beta)$ that cannot be $k$-quasiconformally extended for any $k < \alpha(1 - \beta).$ УДК 517.5 Оцінка норми дошварцової та шварцової похідних деяких унiвалентних функцій Метою цієї статті є отримання оцінок шварцової та дошварцової похідних для сильно зіркоподібних функцій і сильно опуклих функцій порядку $\alpha$ і типу $\beta$. Крім того, наведено приклад функції $f \in S^*(\alpha, \beta)$, яку не можна $k$-квазіконформно поширити для будь-якого $k < \alpha(1 - \beta).$ Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8599 10.3842/umzh.v77i6.8599 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 6 (2025); 445–446 Український математичний журнал; Том 77 № 6 (2025); 445–446 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8599/10537 Copyright (c) 2025 Xiaobin Wu, Wanghao Zhu |
| spellingShingle | Wu, Xiaobin Zhu, Wanghao Wu, Xiaobin Zhu, Wanghao Norm estimation for pre-Schwarzian and Schwarzian derivatives of some univalent functions |
| title | Norm estimation for pre-Schwarzian and Schwarzian derivatives of some univalent functions |
| title_alt | Norm estimation for pre-Schwarzian and Schwarzian derivatives of some univalent functions |
| title_full | Norm estimation for pre-Schwarzian and Schwarzian derivatives of some univalent functions |
| title_fullStr | Norm estimation for pre-Schwarzian and Schwarzian derivatives of some univalent functions |
| title_full_unstemmed | Norm estimation for pre-Schwarzian and Schwarzian derivatives of some univalent functions |
| title_short | Norm estimation for pre-Schwarzian and Schwarzian derivatives of some univalent functions |
| title_sort | norm estimation for pre-schwarzian and schwarzian derivatives of some univalent functions |
| topic_facet | pre-Schwarzian derivative Schwarzian derivative starlike functions convex functions |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8599 |
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