星像函数和凸像函数的逆函数的三阶Hankel行列式

doi:10.13438/j.cnki.jdzk.2021.02.003

吉首大学学报（自然科学版） ›› 2021, Vol. 42 ›› Issue (2): 12-19.DOI: 10.13438/j.cnki.jdzk.2021.02.003

星像函数和凸像函数的逆函数的三阶Hankel行列式

宋园

（滁州职业技术学院基础部，安徽滁州 239000）

出版日期:2021-03-25 发布日期:2021-08-29
作者简介:宋园(1982—)，女，安徽滁州人，滁州职业技术学院基础部讲师，硕士，主要从事复分析及其应用研究.
基金资助:
安徽省教育厅高校自然科学基金项目(KJ2018A0839；KJ2018A0833)；滁州职业技术学院:校级专业（学科）带头人（XD2021006）

Third Order Hankel Determinant for the Inverse of Starlike and Convex Functions

SONG Yuan

(Basic Education Department, Chuzhou Polytechnic, Chuzhou 239000, Anhui China)

Online:2021-03-25 Published:2021-08-29

摘要/Abstract

摘要：用S*表示单位圆盘Δ={z:|z|<1}内满足Re zf′(z) f(z)>0的单叶函数类，K表示单位圆盘Δ={z:|z|<1}内满足Re （1+ zf″(z)′(z)）>0的单叶函数类，利用Toeplitz行列式，得到了f∈S*和f∈K的逆函数的三阶Hankel行列式的上界.

关键词： 单叶函数, 星像函数, 凸像函数, 三阶Hankel行列式, 逆函数, 上界

Abstract: Let S* be the class of functions f univalent in the unit disk Δ={z:|z|<1} such that Re zf′(z)〖〗f(z)>0 (z∈Δ) and let K be the class of functions f univalent in the unit disk Δ={z:|z|<1} such that Re (1+zf″(z)〖〗f′(z))>0 (z∈Δ). Using Toeplitz determinant, we obtian the upper bound of the third order Hankel determinants for the inverse functions of f∈S* and f∈K.

Key words: univalent function, starlike function, convex function, third Hankel determinant, inverse function, upper bound

宋园. 星像函数和凸像函数的逆函数的三阶Hankel行列式[J]. 吉首大学学报（自然科学版）, 2021, 42(2): 12-19.

SONG Yuan. Third Order Hankel Determinant for the Inverse of Starlike and Convex Functions[J]. Journal of Jishou University(Natural Sciences Edition), 2021, 42(2): 12-19.

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星像函数和凸像函数的逆函数的三阶Hankel行列式

Third Order Hankel Determinant for the Inverse of Starlike and Convex Functions

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