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与\(\alpha\)-星像函数相关的某些汉克尔（Hankel）和托普利兹（Toeplitz）行列式不等式

Certain inequalities related with Hankel and Toeplitz determinant for -starlike functions.

作者信息

Gul Ihtesham, Al-Sa'di Sa'ud, Hussain Saqib, Noor Saima

机构信息

Department of Mathematics, COMSATS University Islamabad, Islamabad, 45550, Pakistan.

Government Postgraduate College Mandian, Abbottabad, 22010, Pakistan.

出版信息

Heliyon. 2024 May 16;10(10):e31270. doi: 10.1016/j.heliyon.2024.e31270. eCollection 2024 May 30.

DOI:10.1016/j.heliyon.2024.e31270
PMID:38826701
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11141347/
Abstract

In the present article, we prove the sharp upper bounds for the second order Hankel determinants and related functionals , for -starlike functions. An upper bound for the third order Hankel determinant along with the sharp upper bounds for Toeplitz determinant , where are attained. Many known results are also obtained as corollaries of our main results.

摘要

在本文中，我们证明了关于(\alpha)-星像函数的二阶汉克尔行列式及相关泛函的精确上界。给出了三阶汉克尔行列式的一个上界以及托普利兹行列式(T_n(\varphi))的精确上界，其中(\varphi)为(\alpha)-星像函数。许多已知结果也作为我们主要结果的推论得到。

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