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
Main Authors: Rath, Biswajit, Kumar, K. Sanjay, Krishna, D. Vamshee, Viswanadh, G. K. Surya
Format: Article
Language:English
Published: Institute of Mathematics, NAS of Ukraine 2024
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
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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].
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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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