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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Date:2026
Main Authors: Wu, Xiaobin, Zhu, Wanghao
Format: Article
Language:English
Published: Institute of Mathematics, NAS of Ukraine 2026
Online Access:https://umj.imath.kiev.ua/index.php/umj/article/view/8599
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Journal Title:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
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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 $k < \alpha(1 - \beta).$
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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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AT zhuwanghao normestimationforpreschwarzianandschwarzianderivativesofsomeunivalentfunctions
AT wuxiaobin normestimationforpreschwarzianandschwarzianderivativesofsomeunivalentfunctions
AT zhuwanghao normestimationforpreschwarzianandschwarzianderivativesofsomeunivalentfunctions