Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions
UDC 517.5 We introduce two new subclasses $\mathcal{U}_{\Sigma}(\alpha,\lambda)$ and ${\mathcal{B}_1}_{\Sigma}(\alpha)$ of analytic bi-univalent functions defined in the open unit disk $\mathbb{U}$, which are associated with the Bazilevich functions.  In addition, for funct...
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| Дата: | 2023 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2023
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/6602 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512455625539584 |
|---|---|
| author | Patil, A. B. Shaba, T. G. Patil, A. B. Shaba, T. G. |
| author_facet | Patil, A. B. Shaba, T. G. Patil, A. B. Shaba, T. G. |
| author_sort | Patil, A. B. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-03-06T14:26:58Z |
| description | UDC 517.5
We introduce two new subclasses $\mathcal{U}_{\Sigma}(\alpha,\lambda)$ and ${\mathcal{B}_1}_{\Sigma}(\alpha)$ of analytic bi-univalent functions defined in the open unit disk $\mathbb{U}$, which are associated with the Bazilevich functions.  In addition, for functions that belong to these subclasses, we obtain sharp bounds for the initial Taylor–Maclaurin coefficients $a_2$ and $a_3,$ as well as the sharp estimate for the Fekete–Szegö functional $a_3-\mu a_2^2.$ |
| doi_str_mv | 10.37863/umzh.v75i2.6602 |
| first_indexed | 2026-03-24T03:29:04Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-6602 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:29:04Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-66022023-03-06T14:26:58Z Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions Patil, A. B. Shaba, T. G. Patil, A. B. Shaba, T. G. Analytic function Univalent function Bi-univalent function Starlike function Bazilevic function Fekete-Szego functional Mathematics Analysis UDC 517.5 We introduce two new subclasses $\mathcal{U}_{\Sigma}(\alpha,\lambda)$ and ${\mathcal{B}_1}_{\Sigma}(\alpha)$ of analytic bi-univalent functions defined in the open unit disk $\mathbb{U}$, which are associated with the Bazilevich functions.  In addition, for functions that belong to these subclasses, we obtain sharp bounds for the initial Taylor–Maclaurin coefficients $a_2$ and $a_3,$ as well as the sharp estimate for the Fekete–Szegö functional $a_3-\mu a_2^2.$ УДК 517.5 Точні початкові коефіцієнтні межі та задача  Фекета–Сега для деяких підкласів аналітичних та біодновалентних функцій Введено два нових підкласи $\mathcal{U}_{\Sigma}(\alpha,\lambda)$ і ${\mathcal{B}_1}_{\Sigma}(\alpha)$ аналітичниx біодновалентних функцій, що визначені у відкритому одиничному крузі $\mathbb{U}$ та асоціюються з функціями Базилевича.  Крім того, для функцій, що належать до цих підкласів,  отримано точні межі для початкових коефіцієнтів Тейлора–Маклорена $a_2$ і $a_3$, а також точну оцінку функціонала Фекетa–Сега $a_3-\mu a_2 ^2.$ Institute of Mathematics, NAS of Ukraine 2023-03-02 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/6602 10.37863/umzh.v75i2.6602 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 2 (2023); 198 - 206 Український математичний журнал; Том 75 № 2 (2023); 198 - 206 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/6602/9795 Copyright (c) 2023 Amol Patil, Timilehin Shaba |
| spellingShingle | Patil, A. B. Shaba, T. G. Patil, A. B. Shaba, T. G. Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions |
| title | Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions |
| title_alt | Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions |
| title_full | Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions |
| title_fullStr | Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions |
| title_full_unstemmed | Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions |
| title_short | Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions |
| title_sort | sharp initial coefficient bounds and the fekete–szegö problem for some certain subclasses of analytic and bi-univalent functions |
| topic_facet | Analytic function Univalent function Bi-univalent function Starlike function Bazilevic function Fekete-Szego functional Mathematics Analysis |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6602 |
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