The Fekete-Szegö functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator
In this paper, we introduce and study a new subclass of normalized functions that are analytic and univalent in the open unit disk $ \mathbb{U} = \{z:z\in \mathcal{C}\; \; \text{and}\; \; |z| < 1\}, $ which satisfies the following geometric criterion: $ \begin{equation*} \Re\left(\frac{\m...
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AIMS Press
2023-01-01
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023016?viewType=HTML |
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| author | Hari Mohan Srivastava Timilehin Gideon Shaba Gangadharan Murugusundaramoorthy Abbas Kareem Wanas Georgia Irina Oros |
| author_facet | Hari Mohan Srivastava Timilehin Gideon Shaba Gangadharan Murugusundaramoorthy Abbas Kareem Wanas Georgia Irina Oros |
| author_sort | Hari Mohan Srivastava |
| collection | DOAJ |
| description | In this paper, we introduce and study a new subclass of normalized functions that are analytic and univalent in the open unit disk $ \mathbb{U} = \{z:z\in \mathcal{C}\; \; \text{and}\; \; |z| < 1\}, $ which satisfies the following geometric criterion:
$ \begin{equation*} \Re\left(\frac{\mathcal{L}_{u, v}^{w}f(z)}{z}(1-e^{-2i\phi}\mu^2z^2)e^{i\phi}\right)>0, \end{equation*} $
where $ z\in \mathbb{U} $, $ 0\leqq \mu\leqq 1 $ and $ \phi\in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) $, and which is associated with the Hohlov operator $ \mathcal{L}_{u, v}^{w} $. For functions in this class, the coefficient bounds, as well as upper estimates for the Fekete-Szegö functional and the Hankel determinant, are investigated. |
| first_indexed | 2024-04-11T19:00:23Z |
| format | Article |
| id | doaj.art-16c9394bf0594e6082f939250d011d18 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-11T19:00:23Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-16c9394bf0594e6082f939250d011d182022-12-22T04:08:03ZengAIMS PressAIMS Mathematics2473-69882023-01-018134036010.3934/math.2023016The Fekete-Szegö functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operatorHari Mohan Srivastava0Timilehin Gideon Shaba1Gangadharan Murugusundaramoorthy2Abbas Kareem Wanas3Georgia Irina Oros41. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada 2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan 3. Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan 4. Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy5. Department of Mathematics, University of Ilorin, P.M.B. 1515, Ilorin, Kwara State, Nigeria6. Department of Mathematics, VIT University, Vellore 632014, Tamil Nadu, India7. Department of Mathematics, University of Al-Qadisiyah, Al Diwaniyah, Al-Qadisiyah, Iraq8. Department of Mathematics and Computer Science, University of Oradea, R-410087 Oradea, RomaniaIn this paper, we introduce and study a new subclass of normalized functions that are analytic and univalent in the open unit disk $ \mathbb{U} = \{z:z\in \mathcal{C}\; \; \text{and}\; \; |z| < 1\}, $ which satisfies the following geometric criterion: $ \begin{equation*} \Re\left(\frac{\mathcal{L}_{u, v}^{w}f(z)}{z}(1-e^{-2i\phi}\mu^2z^2)e^{i\phi}\right)>0, \end{equation*} $ where $ z\in \mathbb{U} $, $ 0\leqq \mu\leqq 1 $ and $ \phi\in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) $, and which is associated with the Hohlov operator $ \mathcal{L}_{u, v}^{w} $. For functions in this class, the coefficient bounds, as well as upper estimates for the Fekete-Szegö functional and the Hankel determinant, are investigated.https://www.aimspress.com/article/doi/10.3934/math.2023016?viewType=HTMLanalytic functionsunivalent functionscoefficient boundsfekete-szegöfunctionalhohlov operatordziok-srivastava operatorsrivastava-wright operatorfekete-szegöinequalityhankel determinantbasic q-calculus(p，q)-variation |
| spellingShingle | Hari Mohan Srivastava Timilehin Gideon Shaba Gangadharan Murugusundaramoorthy Abbas Kareem Wanas Georgia Irina Oros The Fekete-Szegö functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator AIMS Mathematics analytic functions univalent functions coefficient bounds fekete-szegöfunctional hohlov operator dziok-srivastava operator srivastava-wright operator fekete-szegöinequality hankel determinant basic q-calculus (p，q)-variation |
| title | The Fekete-Szegö functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator |
| title_full | The Fekete-Szegö functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator |
| title_fullStr | The Fekete-Szegö functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator |
| title_full_unstemmed | The Fekete-Szegö functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator |
| title_short | The Fekete-Szegö functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator |
| title_sort | fekete szego functional and the hankel determinant for a certain class of analytic functions involving the hohlov operator |
| topic | analytic functions univalent functions coefficient bounds fekete-szegöfunctional hohlov operator dziok-srivastava operator srivastava-wright operator fekete-szegöinequality hankel determinant basic q-calculus (p，q)-variation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023016?viewType=HTML |
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