Bound Associated with Certain Hankel Determinants and Zalcman Conjecture for Multivalent Functions of Bounded Turning
In this paper, we investigate for a sharp upper bound to certain generalized second Hankel determinant, the Zalcman conjecture and an upper bound for the third, fourth Hankel determinants for the class of multivalent analytic bounded turning functions. Further, we estimate an upper bound for third a...
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| Language: | English |
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University of Maragheh
2024-07-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_711319_a7ea38045c8975e8e85f5c48a9391bfa.pdf |
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| author | Deekonda Vamshee Krishna Nallamothu Vani Biswajit Rath Karri Sanjay Kumar |
| author_facet | Deekonda Vamshee Krishna Nallamothu Vani Biswajit Rath Karri Sanjay Kumar |
| author_sort | Deekonda Vamshee Krishna |
| collection | DOAJ |
| description | In this paper, we investigate for a sharp upper bound to certain generalized second Hankel determinant, the Zalcman conjecture and an upper bound for the third, fourth Hankel determinants for the class of multivalent analytic bounded turning functions. Further, we estimate an upper bound for third and fourth Hankel determinants with respect to two-fold and three-fold symmetric functions belongs to the same class. The practical tools applied in deriving of our main results are the coefficient inequalities of the Carath$\acute{e}$odory class $\mathcal{P}.$ |
| format | Article |
| id | doaj-art-24310bd447304f408bece58485fba91a |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-24310bd447304f408bece58485fba91a2025-02-11T05:27:31ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-07-0121312714610.22130/scma.2023.1986093.1227711319Bound Associated with Certain Hankel Determinants and Zalcman Conjecture for Multivalent Functions of Bounded TurningDeekonda Vamshee Krishna0Nallamothu Vani1Biswajit Rath2Karri Sanjay Kumar3Department of Mathematics, North-Eastern Hill University (NEHU), Umshing Mawkynroh, Meghalaya-793022, Shillong, Bharat.Department of Mathematics, GITAM School of Science, GITAM University, Andhra Pradesh-530045, Visakhapatnam, India.Department of Mathematics, GITAM School of Science, GITAM University, Andhra Pradesh-530045, Visakhapatnam, India.Department of Mathematics, GITAM School of Science, GITAM University, Andhra Pradesh-530045, Visakhapatnam, India.In this paper, we investigate for a sharp upper bound to certain generalized second Hankel determinant, the Zalcman conjecture and an upper bound for the third, fourth Hankel determinants for the class of multivalent analytic bounded turning functions. Further, we estimate an upper bound for third and fourth Hankel determinants with respect to two-fold and three-fold symmetric functions belongs to the same class. The practical tools applied in deriving of our main results are the coefficient inequalities of the Carath$\acute{e}$odory class $\mathcal{P}.$https://scma.maragheh.ac.ir/article_711319_a7ea38045c8975e8e85f5c48a9391bfa.pdfp-valent bounded turning functionupper boundhankel determinantunivalent functioncarath´eodory functionhypergeometric function |
| spellingShingle | Deekonda Vamshee Krishna Nallamothu Vani Biswajit Rath Karri Sanjay Kumar Bound Associated with Certain Hankel Determinants and Zalcman Conjecture for Multivalent Functions of Bounded Turning Sahand Communications in Mathematical Analysis p-valent bounded turning function upper bound hankel determinant univalent function carath´eodory function hypergeometric function |
| title | Bound Associated with Certain Hankel Determinants and Zalcman Conjecture for Multivalent Functions of Bounded Turning |
| title_full | Bound Associated with Certain Hankel Determinants and Zalcman Conjecture for Multivalent Functions of Bounded Turning |
| title_fullStr | Bound Associated with Certain Hankel Determinants and Zalcman Conjecture for Multivalent Functions of Bounded Turning |
| title_full_unstemmed | Bound Associated with Certain Hankel Determinants and Zalcman Conjecture for Multivalent Functions of Bounded Turning |
| title_short | Bound Associated with Certain Hankel Determinants and Zalcman Conjecture for Multivalent Functions of Bounded Turning |
| title_sort | bound associated with certain hankel determinants and zalcman conjecture for multivalent functions of bounded turning |
| topic | p-valent bounded turning function upper bound hankel determinant univalent function carath´eodory function hypergeometric function |
| url | https://scma.maragheh.ac.ir/article_711319_a7ea38045c8975e8e85f5c48a9391bfa.pdf |
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