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
Main Authors: Kumar, S. Sivaprasad, Yadav, Pooja
Format: Article
Language:English
Published: Institute of Mathematics, NAS of Ukraine 2026
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
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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.
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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
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