关于对称点的星形函数逆的第三汉克尔行列式的锐界

Q3 Mathematics

Matematychni Studii Pub Date : 2022-10-31 DOI:10.30970/ms.58.1.45-50

B. Ráth, D. V. Krishna, K. S. Kumar, G. K. S. Viswanadh

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引用次数: 3

摘要

当反函数$f$属于关于对称点的星形函数的一类时，我们研究了它的第三个Hankel行列式的尖锐界。设$\mathcal{S}^{\ast}_{s}$为关于对称点的一类星形函数。在本文中证明了以下命题(定理):如果$f\in \mathcal{S}^{\ast}_{s}$则\begin{equation*}\big|H_{3,1}(f^{-1})\big|\leq1,\end{equation*}，结果是尖锐的 $f(z)=z/(1-z^2).$

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The sharp bound of the third Hankel determinants for inverse of starlike functions with respect to symmetric points

We study the sharp bound for the third Hankel determinant for the inverse function $f$, when it belongs to of the class of starlike functions with respect to symmetric points.Let $\mathcal{S}^{\ast}_{s}$ be the class of starlike functions with respect to symmetric points. In the article proves the following statements (Theorem): If $f\in \mathcal{S}^{\ast}_{s}$ then\begin{equation*}\big|H_{3,1}(f^{-1})\big|\leq1,\end{equation*}and the result is sharp for $f(z)=z/(1-z^2).$

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来源期刊

Matematychni Studii Mathematics-Mathematics (all)

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal is devoted to research in all fields of mathematics.