两类解析函数的三阶Hankel行列式的上界估计

郭栋; 汤获; 文传军; 李宗涛

doi:10.6054/j.jscnun.2024014

两类解析函数的三阶Hankel行列式的上界估计

郭栋^1, ,,
汤获²,
文传军¹,
李宗涛³

1.
扬州市职业大学数学科学学院，扬州 225009
2.
赤峰学院数学与统计学院，赤峰 024000
3.
广州民航职业技术学院人文社科学院，广州 510403

基金项目:

国家自然科学基金项目 11561001

安徽省高校自然科学基金项目 KJ2018A0833

安徽省高校自然科学基金项目 KJ2020A0993

安徽省高校自然科学基金项目 KJ2020ZD74

内蒙古自治区高等学校科学研究项目 NJZY19211

详细信息

通讯作者:
郭栋, Email: gd791217@163.com

中图分类号: O174.51
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- 文章访问数: 51
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出版历程
- 收稿日期: 2022-10-27
- 网络出版日期: 2024-04-29
- 刊出日期: 2024-02-24

The Upper Bounds of the Third Hankel Determinant for Two Subclasses of Analytic Functions

1.
School of Mathematical Sciences, Yangzhou Polytechnic College, Yangzhou 225009, China
2.
School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China
3.
Faculty of Humanities and Social Sciences, Guangzhou Civil Aviation College, Guangzhou 510403, China

摘要

摘要:
令H表示形如 $f(z)=z+a_2 z^2+a_3 z^3+\cdots$ 且在 $U=\{z:|z|<1\}$ 内解析的函数类，研究了在单位圆盘上的2类解析函数类 $\mathrm{ST}_{\mathrm{s}}=\left\{f ? H: \operatorname{Re} \frac{2 z f^{\prime}(z)}{f(z)-f(-z)}>0, z ? U\right\}$ 和 $R\left(\frac{1}{2}\right)=\left\{f ? H: \operatorname{Re} \frac{f(z)}{z}>\frac{1}{2}, z ? U\right\}$ 的三阶Hankel行列式 $\left|H_{3, 1}(f)\right|$ 的上界估计。
- 解析函数 /
- 有关对称点的星像函数类 /
- 三阶Hankel行列式
Abstract: Let H denote the family of all analytic functions with the form $f(z)=z+a_2 z^2+a_3 z^3+\cdots$ in the unit disk $U=\{z:|z|<1\}$ . Two subclasses of analytic functions ST_s and R(1/2) which are difined in the unit disk U are introduced, respectively, i.e., $\mathrm{ST}_{\mathrm{s}}=\left\{f ? H: \operatorname{Re} \frac{2 z f^{\prime}(z)}{f(z)-f(-z)}>0, z ? U\right\}, R\left(\frac{1}{2}\right)=\left\{f ? H: \operatorname{Re} \frac{f(z)}{z}>\frac{1}{2}, z ? U\right\}.$ And the bounds of $\left|H_{3, 1}(f)\right|$ for subfamilies of ST_s and R(1/2) are obtained.
- analytic function /
- starlike functions with respect to symmetric points /
- third Hankel determinant

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参考文献(17)

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