The Fekete–Szegö functional associated with $m$-th root transformation using conical domains
UDC 517.5 Let $\mathcal{A}$ be the class of analytic functions in the open unit disk  $\mathbb{U}=\{z\in \mathbb{C}\colon |z|<1\}.$  Let $\mathcal{R}_{\alpha }^{p}$ be the operator  defined on $\mathcal{A}$ by&a...
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| Date: | 2024 |
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| 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/7539 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512682285727744 |
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| author | Gurusamy, P. Çağlar, M. Sivasubramanian, S. Cotirla, L. I. Gurusamy, P. Çağlar, M. Sivasubramanian, S. Cotirla, L. I. |
| author_facet | Gurusamy, P. Çağlar, M. Sivasubramanian, S. Cotirla, L. I. Gurusamy, P. Çağlar, M. Sivasubramanian, S. Cotirla, L. I. |
| author_sort | Gurusamy, P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-08-10T06:39:16Z |
| description | UDC 517.5
Let $\mathcal{A}$ be the class of analytic functions in the open unit disk  $\mathbb{U}=\{z\in \mathbb{C}\colon |z|<1\}.$  Let $\mathcal{R}_{\alpha }^{p}$ be the operator  defined on $\mathcal{A}$ by  \begin{equation*}\mathcal{R}_{\alpha }^{p}=f(z) \ast \frac{z}{{{{({1-z})}^{2({1-\alpha })}}}}.\end{equation*} A function $f$ in $\mathcal{A}$ is said to be in the class $k$-$\mathcal{SP}_{\alpha }^{p}$ if $\mathcal{R}_{\alpha }^{p}(f) $ is a $k$-parabolic starlike function.   We focus on the Fekete–Szegö inequality associated with $m$-th root transformation using conical domains for this class. |
| doi_str_mv | 10.3842/umzh.v76i7.7539 |
| first_indexed | 2026-03-24T03:32:40Z |
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| id | umjimathkievua-article-7539 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:40Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-75392024-08-10T06:39:16Z The Fekete–Szegö functional associated with $m$-th root transformation using conical domains The Fekete–Szegö functional associated with $m$-th root transformation using conical domains Gurusamy, P. Çağlar, M. Sivasubramanian, S. Cotirla, L. I. Gurusamy, P. Çağlar, M. Sivasubramanian, S. Cotirla, L. I. Analytic functions Univalent functions prestarlike functions Fekete-Szegö Inequality 30C45 33C15 UDC 517.5 Let $\mathcal{A}$ be the class of analytic functions in the open unit disk  $\mathbb{U}=\{z\in \mathbb{C}\colon |z|<1\}.$  Let $\mathcal{R}_{\alpha }^{p}$ be the operator  defined on $\mathcal{A}$ by  \begin{equation*}\mathcal{R}_{\alpha }^{p}=f(z) \ast \frac{z}{{{{({1-z})}^{2({1-\alpha })}}}}.\end{equation*} A function $f$ in $\mathcal{A}$ is said to be in the class $k$-$\mathcal{SP}_{\alpha }^{p}$ if $\mathcal{R}_{\alpha }^{p}(f) $ is a $k$-parabolic starlike function.   We focus on the Fekete–Szegö inequality associated with $m$-th root transformation using conical domains for this class. УДК 517.5 Функціонал Фекете–Сегьо, асоційований з $m$-м кореневим перетворенням із використанням конічних областей  Нехай $\mathcal{A}$ – клас аналітичних функцій у відкритому одиничному диску $\mathbb{U}=\{z\in \mathbb{C}\colon |z|<1\},$ а $\mathcal{R}_{\alpha }^{p}$ – оператор, визначений на $\mathcal{A}$ за допомогою формули \begin{equation*}\mathcal{R}_{\alpha }^{p}=f(z) \ast \frac{z}{{{{({1-z})}^{2({1-\alpha })}}}}. \end{equation*} Кажуть, що функція $f$ з $\mathcal{A}$ належить до класу $k$-$\mathcal{SP}_{\alpha }^{p}$, якщо $\mathcal{R}_{\alpha }^{p}(f)$ є $k$-параболічною зіркоподібною функцією. Наша увага сфокусована на нерівності Фекете–Сегьо, що асоційована з перетворенням $m$-го кореня з використанням конічних областей для цього класу.  Institute of Mathematics, NAS of Ukraine 2024-08-04 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7539 10.3842/umzh.v76i7.7539 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 7 (2024); 951 - 964 Український математичний журнал; Том 76 № 7 (2024); 951 - 964 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7539/10051 Copyright (c) 2024 Murat Çağlar |
| spellingShingle | Gurusamy, P. Çağlar, M. Sivasubramanian, S. Cotirla, L. I. Gurusamy, P. Çağlar, M. Sivasubramanian, S. Cotirla, L. I. The Fekete–Szegö functional associated with $m$-th root transformation using conical domains |
| title | The Fekete–Szegö functional associated with $m$-th root transformation using conical domains |
| title_alt | The Fekete–Szegö functional associated with $m$-th root transformation using conical domains |
| title_full | The Fekete–Szegö functional associated with $m$-th root transformation using conical domains |
| title_fullStr | The Fekete–Szegö functional associated with $m$-th root transformation using conical domains |
| title_full_unstemmed | The Fekete–Szegö functional associated with $m$-th root transformation using conical domains |
| title_short | The Fekete–Szegö functional associated with $m$-th root transformation using conical domains |
| title_sort | fekete–szegö functional associated with $m$-th root transformation using conical domains |
| topic_facet | Analytic functions Univalent functions prestarlike functions Fekete-Szegö Inequality 30C45 33C15 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7539 |
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