Sufficient conditions and radius problems for the Silverman class
UDC 517.5 For $0<\alpha\leq1$ and $\lambda>0,$ let \begin{equation}\label{1} G_{\lambda,\alpha}=\left\{f\in\mathcal{A}\colon \left|\frac{1-\alpha+\alpha zf''(z)/f'(z)}{z f'(z)/f(z)}-(1-\alpha)\right|<\lambda,\ z\in\mat...
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| Date: | 2024 |
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| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2024
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7317 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512649670819840 |
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| author | Kumar, S. Sivaprasad Priyanka, Priyanka Kumar, S. Sivaprasad Goel, Priyanka |
| author_facet | Kumar, S. Sivaprasad Priyanka, Priyanka Kumar, S. Sivaprasad Goel, Priyanka |
| author_sort | Kumar, S. Sivaprasad |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:35:17Z |
| description | UDC 517.5
For $0<\alpha\leq1$ and $\lambda>0,$ let \begin{equation}\label{1} G_{\lambda,\alpha}=\left\{f\in\mathcal{A}\colon \left|\frac{1-\alpha+\alpha zf''(z)/f'(z)}{z f'(z)/f(z)}-(1-\alpha)\right|<\lambda,\ z\in\mathbb{D}\right\}.\tag{0.1}\end{equation} The general form of the Silverman class introduced by Tuneski and Irmak [Int. J. Math. and Math. Sci., {\bf 2006}, Article~ID 38089 (2006)].  Our differential inequality formulation lays out several sufficient conditions for this class.  Further, we consider a class $\Omega$ given by \begin{equation}\label{omega}\Omega=\left\{f\in\mathcal{A}\colon  |zf'(z)-f(z)|<\frac{1}{2},\ z\in\mathbb{D}\right\}.\tag{0.2}\end{equation} For these two classes, we establish inclusion relations involving some well-known subclasses of $\mathcal{S}^*$ and compute radius estimates featuring various pairings of these classes. |
| doi_str_mv | 10.3842/umzh.v76i3.7317 |
| first_indexed | 2026-03-24T03:32:09Z |
| format | Article |
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| id | umjimathkievua-article-7317 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:09Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-73172024-06-19T00:35:17Z Sufficient conditions and radius problems for the Silverman class Sufficient conditions and radius problems for the Silverman class Kumar, S. Sivaprasad Priyanka, Priyanka Kumar, S. Sivaprasad Goel, Priyanka Silverman class, starlike functions, radius problems UDC 517.5 For $0<\alpha\leq1$ and $\lambda>0,$ let \begin{equation}\label{1} G_{\lambda,\alpha}=\left\{f\in\mathcal{A}\colon \left|\frac{1-\alpha+\alpha zf''(z)/f'(z)}{z f'(z)/f(z)}-(1-\alpha)\right|<\lambda,\ z\in\mathbb{D}\right\}.\tag{0.1}\end{equation} The general form of the Silverman class introduced by Tuneski and Irmak [Int. J. Math. and Math. Sci., {\bf 2006}, Article~ID 38089 (2006)].  Our differential inequality formulation lays out several sufficient conditions for this class.  Further, we consider a class $\Omega$ given by \begin{equation}\label{omega}\Omega=\left\{f\in\mathcal{A}\colon  |zf'(z)-f(z)|<\frac{1}{2},\ z\in\mathbb{D}\right\}.\tag{0.2}\end{equation} For these two classes, we establish inclusion relations involving some well-known subclasses of $\mathcal{S}^*$ and compute radius estimates featuring various pairings of these classes. УДК 517.5 Достатні умови та задачі про радіус для класу Сільвермана Нехай для $0<\alpha\leq1$ і $\lambda>0$  \begin{equation}\label{1} G_{\lambda,\alpha}=\left\{f\in\mathcal{A}\colon  \left|\frac{1-\alpha+\alpha zf''(z)/f'(z)}{z f'(z)/f(z)}-(1-\alpha)\right|<\lambda,\  z\in\mathbb{D}\right\}.\tag{0.1} \end{equation} Загальну форму класу Сільвермана ввели Тунескі та Ірмак [Int. J. Math. and Math. Sci., {\bf 2006}, Article ID 38089 (2006)].  Наше формулювання диференціальної нерівності містить кілька достатніх умов для цього класу.  Крім того, розглянуто клас $\Omega,$ що задається формулою \begin{equation}\label{omega}\Omega=\left\{f\in\mathcal{A}\colon  |zf'(z)-f(z)|<\frac{1}{2},\ z\in\mathbb{D}\right\}.\tag{0.2}\end{equation} Для цих двох класів  встановлено співвідношення включення, що містить деякі відомі підкласи $\mathcal{S}^*,$ і обчислено оцінки радіусів для різних пар класів, що вивчаються.  Institute of Mathematics, NAS of Ukraine 2024-03-25 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7317 10.3842/umzh.v76i3.7317 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 3 (2024); 405 - 422 Український математичний журнал; Том 76 № 3 (2024); 405 - 422 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7317/9859 Copyright (c) 2024 Priyanka Goel, S. Sivaprasad Kumar |
| spellingShingle | Kumar, S. Sivaprasad Priyanka, Priyanka Kumar, S. Sivaprasad Goel, Priyanka Sufficient conditions and radius problems for the Silverman class |
| title | Sufficient conditions and radius problems for the Silverman class |
| title_alt | Sufficient conditions and radius problems for the Silverman class |
| title_full | Sufficient conditions and radius problems for the Silverman class |
| title_fullStr | Sufficient conditions and radius problems for the Silverman class |
| title_full_unstemmed | Sufficient conditions and radius problems for the Silverman class |
| title_short | Sufficient conditions and radius problems for the Silverman class |
| title_sort | sufficient conditions and radius problems for the silverman class |
| topic_facet | Silverman class starlike functions radius problems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7317 |
| work_keys_str_mv | AT kumarssivaprasad sufficientconditionsandradiusproblemsforthesilvermanclass AT priyankapriyanka sufficientconditionsandradiusproblemsforthesilvermanclass AT kumarssivaprasad sufficientconditionsandradiusproblemsforthesilvermanclass AT goelpriyanka sufficientconditionsandradiusproblemsforthesilvermanclass |