A refinement of Schwarz's lemma at the boundary
UDC 517.5 We investigate a boundary version of the Schwarz lemma for analytic functions.  In addition, an analytic function satisfying the equality case is found by deducing inequalities related to the modulus of the derivative of analytic functions at a bounda...
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| Datum: | 2024 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2024
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7364 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512657865441280 |
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| author | Örnek, Bülent Nafi Örnek, Bülent Nafi |
| author_facet | Örnek, Bülent Nafi Örnek, Bülent Nafi |
| author_sort | Örnek, Bülent Nafi |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:35:26Z |
| description | UDC 517.5
We investigate a boundary version of the Schwarz lemma for analytic functions.  In addition, an analytic function satisfying the equality case is found by deducing inequalities related to the modulus of the derivative of analytic functions at a boundary point of the unit disk.  Some coefficients used in the Taylor expansion of the function are considered in these inequalities.  In the last theorem, by analyzing the Taylor expansion about two points, we obtain the modulus of the derivative of the function at point 1. |
| doi_str_mv | 10.3842/umzh.v74i4.7364 |
| first_indexed | 2026-03-24T03:32:17Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7364 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:17Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-73642024-06-19T00:35:26Z A refinement of Schwarz's lemma at the boundary A refinement of Schwarz's lemma at the boundary Örnek, Bülent Nafi Örnek, Bülent Nafi Analytic function Angular derivative Schwarz lemma 30C80 UDC 517.5 We investigate a boundary version of the Schwarz lemma for analytic functions.  In addition, an analytic function satisfying the equality case is found by deducing inequalities related to the modulus of the derivative of analytic functions at a boundary point of the unit disk.  Some coefficients used in the Taylor expansion of the function are considered in these inequalities.  In the last theorem, by analyzing the Taylor expansion about two points, we obtain the modulus of the derivative of the function at point 1. УДК 517.5 Уточнення леми Шварца на межі Досліджено граничну версію леми Шварца для аналітичних функцій. Крім того, аналітичну функцію, що задовольняє випадок рівності, знайдено шляхом отримання нерівностей, які пов’язані з модулем похідної аналітичних функцій у певній граничній точці  одиничного круга.  В  цих нерівностях розглядаються деякі коефіцієнти, що використовуються в розкладі Тейлора даної функції.  В останній теоремі, враховуючи розклад Тейлора в околі двох точок, отримано модуль похідної функції в точці 1. Institute of Mathematics, NAS of Ukraine 2024-04-26 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7364 10.3842/umzh.v74i4.7364 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 4 (2024); 515 - 524 Український математичний журнал; Том 76 № 4 (2024); 515 - 524 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7364/9913 Copyright (c) 2024 Bülent Nafi |
| spellingShingle | Örnek, Bülent Nafi Örnek, Bülent Nafi A refinement of Schwarz's lemma at the boundary |
| title | A refinement of Schwarz's lemma at the boundary |
| title_alt | A refinement of Schwarz's lemma at the boundary |
| title_full | A refinement of Schwarz's lemma at the boundary |
| title_fullStr | A refinement of Schwarz's lemma at the boundary |
| title_full_unstemmed | A refinement of Schwarz's lemma at the boundary |
| title_short | A refinement of Schwarz's lemma at the boundary |
| title_sort | refinement of schwarz's lemma at the boundary |
| topic_facet | Analytic function Angular derivative Schwarz lemma 30C80 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7364 |
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