伯努利双纽线右半有界区域内广义解析函数类的三阶Hankel行列式  

Third Hankel determinant for a class of generalized analytic functions on the right-half bounded domain of lemniscate of Bernoulli

作　　者：汤获[1] 张海燕[1] 牛潇萌[1] TANG Huo;ZHANG Haiyan;NIU Xiaomeng(School of Mathematics and Statistics,Chifeng University, Chifeng 024000,China)

机构地区：[1]赤峰学院数学与统计学院

出　　处：《中山大学学报（自然科学版）》2019年第3期103-109,共7页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11561001,11271045);内蒙古高校青年科技英才支持计划(NJYT-18-A14);内蒙古自然科学基金(2018MS01026);内蒙古高等学校科研项目(NJZY17300,NJZY18217);赤峰市自然科学研究课题

摘　　要：设A表示在单位圆盘D={z:|z|<1}内解析且满足f(0)=f′(0)-1=0的函数类。首先,引入伯努利双纽线右半有界区域内的广义解析函数类SRλ^*:SRλ^*=f∈A:(1-λ)f(z)z+λf′(z)1+z(0≤λ≤1;z∈D)。然后,讨论上述函数类SRλ^*的三阶Hankel行列式H3(1),得到其上界估计。Let A be the class of analytic functions f(z) in the unit disc D={z:|z|<1} normalized by f(0)=f ′(0)-1=0 . A class of generalized analytic functions SRλ^* on the right-half bounded domain of lemniscate of Bernoulli is introduced, which is shown as follows: SRλ^*= f∈A:(1-λ) f(z) z +λf ′(z) 1+z (0≤λ≤1;z∈D). And, the third Hankel determinant H 3(1) for the above function class SRλ^* is investigated and the upper bound for the above determinant H 3(1) is obtained.

关 键 词：伯努利双纽线 广义解析函数 三阶Hankel行列式 上界估计 

分 类 号：O174.5[理学—数学]