| 某类解析函数的三阶Hankel行列式 |
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| 引用本文： | 郭栋, 汤获, 文传军, 李宗涛. 两类解析函数的三阶Hankel行列式的上界估计[J]. 华南师范大学学报（自然科学版）, 2024, 56(1): 118-122. DOI: 10.6054/j.jscnun.2024014 |
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| 作者姓名： | 郭栋 汤获 文传军 李宗涛 |
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| 作者单位： | 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 |
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| 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, KJ2020A0993，KJ2020ZD74); 内蒙古自治区高等学校科学研究项目(NJZY19211) |
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| 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$mathrm{ST}_{mathrm{s}}=left{f ? H: operatorname{Re} frac{2 z f^{prime}(z)}{f(z)-f(-z)}>0, z ? Uright}$和$Rleft(frac{1}{2}right)=left{f ? H: operatorname{Re} frac{f(z)}{z}>frac{1}{2}, z ? Uright}$的三阶Hankel行列式$left|H_{3, 1}(f)right|$的上界估计。
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| 关 键 词： | 解析函数 有关对称点的星像函数类 三阶Hankel行列式 |
| 收稿时间： | 2022-10-28 |
On the coefficients and Hankel determinants of univalent functions |
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| GUO Dong, TANG Huo, WEN Chuanjun, LI Zongtao. The Upper Bounds of the Third Hankel Determinant for Two Subclasses of Analytic Functions[J]. Journal of South China Normal University (Natural Science Edition), 2024, 56(1): 118-122. DOI: 10.6054/j.jscnun.2024014 |
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| Authors: | GUO Dong TANG Huo WEN Chuanjun LI Zongtao |
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| Affiliation: | 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 |
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| 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 STs and R(1/2) which are difined in the unit disk U are introduced, respectively, i.e., t t tt $ mathrm{ST}_{mathrm{s}}=left{f ? H: operatorname{Re} frac{2 z f^{prime}(z)}{f(z)-f(-z)}>0, z ? Uright}, Rleft(frac{1}{2}right)=left{f ? H: operatorname{Re} frac{f(z)}{z}>frac{1}{2}, z ? Uright}. $tt t And the bounds of $left|H_{3, 1}(f)right|$ for subfamilies of STs and R(1/2) are obtained. |
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| Keywords: | analytic function starlike functions with respect to symmetric points third Hankel determinant |
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