Sharp starlike and convex radius for the differential operator of analytic functions
UDC 517.5 Under given coefficient conditions for analytic functions $f$ in the unit disk $\mathbf{D}$, we first obtain the starlike and convex radius  for the linear  combination of the differential operator  $zf'$ of analytic functions $f...
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| Date: | 2025 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2025
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7788 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512748354404352 |
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| author | Hu, Zhenyong Srivastava, H. M. Zhang, Ying Hu, Zhenyong Srivastava, H. M. Zhang, Ying |
| author_facet | Hu, Zhenyong Srivastava, H. M. Zhang, Ying Hu, Zhenyong Srivastava, H. M. Zhang, Ying |
| author_sort | Hu, Zhenyong |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-05-09T12:53:52Z |
| description | UDC 517.5
Under given coefficient conditions for analytic functions $f$ in the unit disk $\mathbf{D}$, we first obtain the starlike and convex radius  for the linear  combination of the differential operator  $zf'$ of analytic functions $f$ in $\mathbf{D}.$ Then we obtain the starlike and convex radius  for the differential operator  $zf'$.  Furthermore, we present the starlike and convex radius  for the linear  combination of the differential operator  $zf'$  and analytic functions  $f$ in $\mathbf{D}$.  Our results imply the related result obtained by Gavrilov [Mat. Zametki, 7, 295–298 (1970)]. |
| doi_str_mv | 10.3842/umzh.v76i10.7788 |
| first_indexed | 2026-03-24T03:33:43Z |
| format | Article |
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| id | umjimathkievua-article-7788 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:33:43Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-77882025-05-09T12:53:52Z Sharp starlike and convex radius for the differential operator of analytic functions Sharp starlike and convex radius for the differential operator of analytic functions Hu, Zhenyong Srivastava, H. M. Zhang, Ying Hu, Zhenyong Srivastava, H. M. Zhang, Ying analytic functions; starlike functions; convex functions; differential operator. UDC 517.5 Under given coefficient conditions for analytic functions $f$ in the unit disk $\mathbf{D}$, we first obtain the starlike and convex radius  for the linear  combination of the differential operator  $zf'$ of analytic functions $f$ in $\mathbf{D}.$ Then we obtain the starlike and convex radius  for the differential operator  $zf'$.  Furthermore, we present the starlike and convex radius  for the linear  combination of the differential operator  $zf'$  and analytic functions  $f$ in $\mathbf{D}$.  Our results imply the related result obtained by Gavrilov [Mat. Zametki, 7, 295–298 (1970)]. УДК 517.5 Точний зіркоподібний та опуклий радіус для диференціального оператора аналітичних функцій При заданих коефіцієнтних умовах для аналітичних функцій $f$ в одиничному крузі $\mathbf{D}$ спочатку отримано зіркоподібний та опуклий радіус для лінійної комбінації диференціального оператора $zf'$ аналітичних функцій $f$ в $\mathbf{D}$. Після цого одержано зіркоподібний та опуклий радіус для диференціального оператора $zf'$. Крім того, наведено зіркоподібний та опуклий радіус для лінійної комбінації диференціального оператора $zf'$ та аналітичних функцій $f$ в $\mathbf{D}$. З цих результатів випливає відповідний результат Гаврилова [Mat.\ Zametki, 7 295–298 (1970)]. Institute of Mathematics, NAS of Ukraine 2025-05-07 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7788 10.3842/umzh.v76i10.7788 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 10 (2024); 1455 - 1462 Український математичний журнал; Том 76 № 10 (2024); 1455 - 1462 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7788/10213 Copyright (c) 2024 Zhenyong Hu, H.M. Srivastava, Ying Zhang |
| spellingShingle | Hu, Zhenyong Srivastava, H. M. Zhang, Ying Hu, Zhenyong Srivastava, H. M. Zhang, Ying Sharp starlike and convex radius for the differential operator of analytic functions |
| title | Sharp starlike and convex radius for the differential operator of analytic functions |
| title_alt | Sharp starlike and convex radius for the differential operator of analytic functions |
| title_full | Sharp starlike and convex radius for the differential operator of analytic functions |
| title_fullStr | Sharp starlike and convex radius for the differential operator of analytic functions |
| title_full_unstemmed | Sharp starlike and convex radius for the differential operator of analytic functions |
| title_short | Sharp starlike and convex radius for the differential operator of analytic functions |
| title_sort | sharp starlike and convex radius for the differential operator of analytic functions |
| topic_facet | analytic functions starlike functions convex functions differential operator. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7788 |
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