Sharp Coefficient Results on the Inverse of Silverman Starlike Functions

Pub Date : 2024-08-09 DOI:10.3103/s1068362324700213

L. Shi, M. Arif

引用次数: 0

Abstract

In the present paper, we consider a subclass of starlike functions \(\mathcal{G}_{\mu}\) introduced by Silverman. It is defined by the ratio of analytic representations of convex and starlike functions. The main aim is to determine the sharp bounds of coefficient problems for the inverse of functions in this class. We derive the upper bounds of some initial coefficients, the Fekete–Szegö type inequality and the second Hankel determinant \(\mathcal{H}_{2,2}\left(f^{-1}\right)\) for \(f\in\mathcal{G}_{\mu}\). On the third Hankel determinant \(\mathcal{H}_{3,1}\left(f^{-1}\right)\), we give a bound on the inverse of \(f\in\mathcal{G}\). All the results are proved to be sharp.

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西尔弗曼星状函数逆的锐系数结果

摘要在本文中，我们考虑了西尔弗曼引入的星状函数的一个子类 \(\mathcal{G}_{\mu}\)。它是由凸函数和星状函数的解析表示之比定义的。主要目的是确定该类函数逆的系数问题的尖锐边界。我们推导出了\(f\in\mathcal{G}_\{mu}\)的一些初始系数的上限、费克特-塞戈（Fekete-Szegö）型不等式和第二个汉克尔行列式（\mathcal{H}_{2,2}left(f^{-1}\right)\）。关于第三个汉克尔行列式（(\mathcal{H}_{3,1}\left(f^{-1}\right)），我们给出了\(fin\mathcal{G}\)的逆的约束。所有结果都被证明是尖锐的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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