The sharp bound of the third Hankel determinant for certain subfamilies of analytic functions
UDC 517.5 We study an upper bound and the sharp bound of the third-order Hankel determinant for some subfamilies of analytic functions for the parameters $\alpha\in(1,4/3]$ and $\alpha=3/2,$ respectively, also proving the recent conjecture  for the sharp bounds made in [Vir...
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| Date: | 2024 |
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| Main Authors: | , , , |
| Format: | Article |
| 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/7524 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512680978153472 |
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| author | Rath, Biswajit Kumar, K. Sanjay Krishna, D. Vamshee Viswanadh, G. K. Surya Rath, Biswajit Kumar, K. Sanjay Krishna, D. Vamshee Viswanadh, G. K. Surya |
| author_facet | Rath, Biswajit Kumar, K. Sanjay Krishna, D. Vamshee Viswanadh, G. K. Surya Rath, Biswajit Kumar, K. Sanjay Krishna, D. Vamshee Viswanadh, G. K. Surya |
| author_sort | Rath, Biswajit |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-08-10T06:39:15Z |
| description | UDC 517.5
We study an upper bound and the sharp bound of the third-order Hankel determinant for some subfamilies of analytic functions for the parameters $\alpha\in(1,4/3]$ and $\alpha=3/2,$ respectively, also proving the recent conjecture  for the sharp bounds made in [Virendra Kumar, Sushil Kumar, V. Ravichandran, Third Hankel determinant for certain classes of analytic functions, Mathematical Analysis I: Approximation Theory, February (2020); DOI: 10.1007/978-981-15-1153-019]. |
| doi_str_mv | 10.3842/umzh.v76i7.7524 |
| first_indexed | 2026-03-24T03:32:39Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7524 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:39Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-75242024-08-10T06:39:15Z The sharp bound of the third Hankel determinant for certain subfamilies of analytic functions The sharp bound of the third Hankel determinant for certain subfamilies of analytic functions Rath, Biswajit Kumar, K. Sanjay Krishna, D. Vamshee Viswanadh, G. K. Surya Rath, Biswajit Kumar, K. Sanjay Krishna, D. Vamshee Viswanadh, G. K. Surya Analytic function Upper bound Hankel determinant Carath´eodory function UDC 517.5 We study an upper bound and the sharp bound of the third-order Hankel determinant for some subfamilies of analytic functions for the parameters $\alpha\in(1,4/3]$ and $\alpha=3/2,$ respectively, also proving the recent conjecture  for the sharp bounds made in [Virendra Kumar, Sushil Kumar, V. Ravichandran, Third Hankel determinant for certain classes of analytic functions, Mathematical Analysis I: Approximation Theory, February (2020); DOI: 10.1007/978-981-15-1153-019]. УДК 517.5 Точна границя для третього визначника Ганкеля  для деяких підсімей аналітичних функцій Досліджено верхню та точну границю визначника Ганкеля третього порядку для певних підсімей аналітичних функцій та параметрів $\alpha\in(1,4/3]$ та $\alpha=3/2,$ відповідно, а також доведено нещодавню гіпотезу  для точних границь, наведену в [Virendra Kumar, Sushil Kumar, V. Ravichandran, Third Hankel determinant for certain classes of analytic functions, Mathematical Analysis I: Approximation Theory, February (2020); DOI: 10.1007/978-981-15-1153-019]. Institute of Mathematics, NAS of Ukraine 2024-08-04 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7524 10.3842/umzh.v76i7.7524 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 7 (2024); 1024 - 1040 Український математичний журнал; Том 76 № 7 (2024); 1024 - 1040 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7524/10058 Copyright (c) 2024 Biswajit Rath |
| spellingShingle | Rath, Biswajit Kumar, K. Sanjay Krishna, D. Vamshee Viswanadh, G. K. Surya Rath, Biswajit Kumar, K. Sanjay Krishna, D. Vamshee Viswanadh, G. K. Surya The sharp bound of the third Hankel determinant for certain subfamilies of analytic functions |
| title | The sharp bound of the third Hankel determinant for certain subfamilies of analytic functions |
| title_alt | The sharp bound of the third Hankel determinant for certain subfamilies of analytic functions |
| title_full | The sharp bound of the third Hankel determinant for certain subfamilies of analytic functions |
| title_fullStr | The sharp bound of the third Hankel determinant for certain subfamilies of analytic functions |
| title_full_unstemmed | The sharp bound of the third Hankel determinant for certain subfamilies of analytic functions |
| title_short | The sharp bound of the third Hankel determinant for certain subfamilies of analytic functions |
| title_sort | sharp bound of the third hankel determinant for certain subfamilies of analytic functions |
| topic_facet | Analytic function Upper bound Hankel determinant Carath´eodory function |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7524 |
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