特定阶的Toeplitz行列式的精确界，与Bernoulli的lemnisate相关的函数的Zalcman猜想和Krushkals不等式

IF 0.9 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2025-02-13 DOI:10.1016/j.bulsci.2025.103585

Winne Bareh , D. Vamshee Krishna , Biswajit Rath

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引用次数: 0

摘要

本文的主要目的是研究开单位盘D上归一化解析函数的Toeplitz定阶行列式、Zalcman猜想和Krushkals不等式的尖锐界，并与我们所熟悉的星状函数亚族有关。在我们的主要结果的推导中所应用的实用工具是carath odory P类的系数不等式。

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Exact bounds to the Toeplitz determinants of certain order, Zalcman conjecture and Krushkals inequalities for the functions associated with the lemniscate of Bernoulli

The main object of this article is to investigate sharp bounds of the Toeplitz determinants of certain order, Zalcman conjecture and Krushkals inequalities for normalized analytic functions in the open unit disk

D

, associated with the familiar subfamily of starlike functions associated with the right half of lemniscate of Bernoulli. The practical tools applied in the derivation of our main results are the coefficient inequalities of the Carathéodory class