On applications of the extended Jack's lemma
UDC 517.5 We introduce and study a class ${\bf\mathcal{G}}(\alpha,\beta)$ comprising analytic functions associated with a sector domain, where $\alpha,\beta\in(0,1]$. By using the extended version of Jack's lemma, we deduce the Open–Door lemma sufficient conditions for functions to be in $...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8419 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513067482218496 |
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| author | Kumar, S. Sivaprasad Yadav, Pooja Kumar, S. Sivaprasad Yadav, Pooja |
| author_facet | Kumar, S. Sivaprasad Yadav, Pooja Kumar, S. Sivaprasad Yadav, Pooja |
| author_sort | Kumar, S. Sivaprasad |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:39:49Z |
| description | UDC 517.5
We introduce and study a class ${\bf\mathcal{G}}(\alpha,\beta)$ comprising analytic functions associated with a sector domain, where $\alpha,\beta\in(0,1]$. By using the extended version of Jack's lemma, we deduce the Open–Door lemma sufficient conditions for functions to be in ${\bf\mathcal{G}}(\alpha,\beta)$. Furthermore, we present special cases of our results that are in agreement with known results. |
| doi_str_mv | 10.3842/umzh.v77i6.8419 |
| first_indexed | 2026-03-24T03:38:47Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8419 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:38:47Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-84192026-03-21T13:39:49Z On applications of the extended Jack's lemma On applications of the extended Jack's lemma Kumar, S. Sivaprasad Yadav, Pooja Kumar, S. Sivaprasad Yadav, Pooja Analytic function Subordination Jack's lemma Open-Door lemma 30C45 30C80 UDC 517.5 We introduce and study a class ${\bf\mathcal{G}}(\alpha,\beta)$ comprising analytic functions associated with a sector domain, where $\alpha,\beta\in(0,1]$. By using the extended version of Jack's lemma, we deduce the Open–Door lemma sufficient conditions for functions to be in ${\bf\mathcal{G}}(\alpha,\beta)$. Furthermore, we present special cases of our results that are in agreement with known results. УДК 517.5 Про застосування узагальненої леми Джека Уведено та досліджено клас ${\bf\mathcal{G}}(\alpha,\beta)$ аналітичних функцій, пов’язаних із секторною областю, де $\alpha,\beta\in(0,1]$. З використанням узагальненої версії леми Джека отримано достатні умови типу леми Open–Door для належності функцій до класу ${\bf\mathcal{G}}(\alpha,\beta)$. Крім того, наведено окремі випадки, у яких отримані результати узгоджуються з відомими твердженнями. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8419 10.3842/umzh.v77i6.8419 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 6 (2025); 449–450 Український математичний журнал; Том 77 № 6 (2025); 449–450 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8419/10539 Copyright (c) 2025 S. Sivaprasad Kumar, Pooja Yadav |
| spellingShingle | Kumar, S. Sivaprasad Yadav, Pooja Kumar, S. Sivaprasad Yadav, Pooja On applications of the extended Jack's lemma |
| title | On applications of the extended Jack's lemma |
| title_alt | On applications of the extended Jack's lemma |
| title_full | On applications of the extended Jack's lemma |
| title_fullStr | On applications of the extended Jack's lemma |
| title_full_unstemmed | On applications of the extended Jack's lemma |
| title_short | On applications of the extended Jack's lemma |
| title_sort | on applications of the extended jack's lemma |
| topic_facet | Analytic function Subordination Jack's lemma Open-Door lemma 30C45 30C80 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8419 |
| work_keys_str_mv | AT kumarssivaprasad onapplicationsoftheextendedjack039slemma AT yadavpooja onapplicationsoftheextendedjack039slemma AT kumarssivaprasad onapplicationsoftheextendedjack039slemma AT yadavpooja onapplicationsoftheextendedjack039slemma |