Fekete-Szegö and Hankel inequalities for certain class of analytic functions related to the sine function
In this present investigation, the authors obtain Fekete-Szegö inequality for certain normalized analytic function $ f(\zeta) $ defined on the open unit disk for which $ (f'(\zeta)^{\vartheta}\left( \frac{\zeta f'(\zeta )}{f(\zeta )}\right)^{1-\vartheta} \prec 1+\sin \zeta ; \qquad (0\l...
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| Format: | Article |
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AIMS Press
2022-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022354?viewType=HTML |
| _version_ | 1819279177378955264 |
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| author | Huo Tang Gangadharan Murugusundaramoorthy Shu-Hai Li Li-Na Ma |
| author_facet | Huo Tang Gangadharan Murugusundaramoorthy Shu-Hai Li Li-Na Ma |
| author_sort | Huo Tang |
| collection | DOAJ |
| description | In this present investigation, the authors obtain Fekete-Szegö inequality for certain normalized analytic function $ f(\zeta) $ defined on the open unit disk for which
$ (f'(\zeta)^{\vartheta}\left( \frac{\zeta f'(\zeta )}{f(\zeta )}\right)^{1-\vartheta} \prec 1+\sin \zeta ; \qquad (0\leq \vartheta \leq 1) $
lies in a region starlike with respect to $ 1 $ and symmetric with respect to the real axis. As a special case of this result, the Fekete-Szegö inequality for a class of functions defined through Poisson distribution series is obtained. Further, we discuss the second Hankel inequality for functions in this new class. |
| first_indexed | 2024-12-24T00:23:45Z |
| format | Article |
| id | doaj.art-3d5423efa07e440e84c5f424d2ed4b9e |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-24T00:23:45Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-3d5423efa07e440e84c5f424d2ed4b9e2022-12-21T17:24:30ZengAIMS PressAIMS Mathematics2473-69882022-01-01746365638010.3934/math.2022354Fekete-Szegö and Hankel inequalities for certain class of analytic functions related to the sine functionHuo Tang0Gangadharan Murugusundaramoorthy1Shu-Hai Li2Li-Na Ma31. School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, Inner Mongolia, China2. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, Tamilnadu, India1. School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, Inner Mongolia, China1. School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, Inner Mongolia, ChinaIn this present investigation, the authors obtain Fekete-Szegö inequality for certain normalized analytic function $ f(\zeta) $ defined on the open unit disk for which $ (f'(\zeta)^{\vartheta}\left( \frac{\zeta f'(\zeta )}{f(\zeta )}\right)^{1-\vartheta} \prec 1+\sin \zeta ; \qquad (0\leq \vartheta \leq 1) $ lies in a region starlike with respect to $ 1 $ and symmetric with respect to the real axis. As a special case of this result, the Fekete-Szegö inequality for a class of functions defined through Poisson distribution series is obtained. Further, we discuss the second Hankel inequality for functions in this new class.https://www.aimspress.com/article/doi/10.3934/math.2022354?viewType=HTMLanalytic functionstarlike functionsubordinationcoefficient problemfekete-szegöinequalityhankel determinantpoisson distribution series |
| spellingShingle | Huo Tang Gangadharan Murugusundaramoorthy Shu-Hai Li Li-Na Ma Fekete-Szegö and Hankel inequalities for certain class of analytic functions related to the sine function AIMS Mathematics analytic function starlike function subordination coefficient problem fekete-szegöinequality hankel determinant poisson distribution series |
| title | Fekete-Szegö and Hankel inequalities for certain class of analytic functions related to the sine function |
| title_full | Fekete-Szegö and Hankel inequalities for certain class of analytic functions related to the sine function |
| title_fullStr | Fekete-Szegö and Hankel inequalities for certain class of analytic functions related to the sine function |
| title_full_unstemmed | Fekete-Szegö and Hankel inequalities for certain class of analytic functions related to the sine function |
| title_short | Fekete-Szegö and Hankel inequalities for certain class of analytic functions related to the sine function |
| title_sort | fekete szego and hankel inequalities for certain class of analytic functions related to the sine function |
| topic | analytic function starlike function subordination coefficient problem fekete-szegöinequality hankel determinant poisson distribution series |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022354?viewType=HTML |
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