一类与贝努利双纽线和共轭点有关的广义解析函数的三阶Hankel行列式  

Third Hankel Determinant for a Class of Generalized Analytic Functions Associated with Bernoulli’s Lemniscate and Conjugate Points

作　　者：张海燕[1] 汤获[1] 马丽娜[1] ZHANG Hai-yan;TANG Huo;MA Li-na(School of Mathematics and Statistics,Chifeng University,Chifeng Inner Mongolia 024000,China)

机构地区：[1]赤峰学院数学与统计学院

出　　处：《西南大学学报（自然科学版）》2019年第6期73-78,共6页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11561001,11761006);内蒙古高等学校科学研究项目(NJZY16251)

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,引入了与贝努利双纽线有关且具有共轭点的广义解析函数类SL*c(α,μ):SL*c(α,μ)=f∈A:2αμz3f(z)+2(2αμ+α-μ)z2f″(z)+2zf′(z)αμz2(f(z)+f(z))″+(α-μ)z(f(z)+f(z))′+(1-α+μ)(f(z)+f(z))1+z,z∈D然后,讨论了此类函数的三阶Hankel行列式H3(1),得到其上界估计.Let A be the class of analytic functions in the unit disc D ={z:|z|<1} normalized by f(0)= f′(0)-1=0 . First,a class of generalized analytic functions associated with Bernoulli s lemniscate and conjugate points are introduced,which is shown as: SL * c(α,μ)= f∈ A :2αμz3f (z)+2(2αμ+α-μ)z2f″(z)+2zf′(z)αμz2 ( f(z)+ f(z ))″+(α-μ)z ( f(z)+ f(z ))′+(1-α+μ)( f(z)+ f(z ))1+z,z∈ D Then,the third Hankel determinant H3(1) for this function class is investigated and the upper bound of the above determinant is obtained.

关 键 词：解析函数 共轭点 三阶Hankel行列式 贝努利双纽线 上界 

分 类 号：O174.5[理学—数学]