伯努利双纽线右半区域内两类解析函数的优化问题  

Majorization problems for two classes of analytic functions in the right-half of lemniscate of Bernoulli

作　　者：汤获[1] 邓冠铁[2] 牛潇萌[1] 何涛[1] TANG Huo;DENG Guantie;NIU Xiaomeng;HE Tao(School of Mathematics and Statistics,Chifeng University,024000,Chifeng,Inner Mongolia,China;School of Mathematical Sciences,Beijing Normal University,100875,Beijing,China)

机构地区：[1]赤峰学院数学与统计学院,内蒙古赤峰024000 [2]北京师范大学数学科学学院,北京100875

出　　处：《北京师范大学学报（自然科学版）》2020年第1期16-21,共6页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11561001,11271045);内蒙古高校青年科技英才支持计划资助项目(NJYT-18-A14);内蒙古自然科学基金资助项目(2018MS01026);内蒙古高等学校科研基金资助项目(NJZY17300,NJZY17301,NJZY18217);赤峰市自然科学研究课题资助项目。

摘　　要：近些年来,单复变几何函数论中不同区域上解析函数的优化问题备受研究者的关注.本文借助Liu-Owa积分算子和从属关系,分别引入了伯努利双纽线右半区域内一致星象函数类R■(γ,δ)和螺旋函数类S■(a,θ),讨论了其优化问题.所得结果丰富和扩充了单复变几何函数论中的优化理论.Majorization of analytic functions in different domains has attracted much attention in recent years in the field of geometry function theory of one complex variable. We in this paper introduce the class Rαβ,p(γ,δ) of uniformly starlike functions and the class Sα β,p(a,θ) of spirallike functions in the right-half of lemniscate of Bernoulli, as defined using the Liu-Owa integral operator and subordination relationship, and discuss majorization problems for functions belonging to these classes. Our results so obtained enrich and extend the majorization theory in the field of geometry function theory of one complex variable.

关 键 词：解析函数 伯努利双纽线右半区域 Liu-Owa积分算子 从属关系 优化 

分 类 号：O174.5[理学—数学]