摘要
设f=h+g^-是单位圆盘U上的单叶保形复值调和函数,其中h和g在U上解析.利用广义Salagean算子定义和研究一类新的调和函数类,给出该类中函数的充分系数不等式条件,并证明当g系数为负数时,这些条件是充分必要的.由此条件进一步讨论极值点及其相关几何性质,得到新的结果.
A complex-valued harmonic function that is univalent and sense preserving in the unit disk U can be written in the form of f=h+g^-,where h and g are analytic in U.In this paper,we define and investigate a new class of harmonic functions by generalized Salagean operator,the sufficient coefficient inequality conditions of the functions in this class are given,and it is proved that these conditions are necessary and sufficient when the coefficients are negative.Based on this condition,the extreme points and its related geometric properties are further discussed,and new results are obtained.
作者
李玉毛
李书海
马丽娜
LI Yu-mao;LI Shu-hai;MA Li-na(Collage of Mathematics and Computer Science,Chifeng University,Chifeng 024000,China)
出处
《数学的实践与认识》
北大核心
2020年第24期196-204,共9页
Mathematics in Practice and Theory
基金
内蒙古自然科学基金项目(2019MS01023)
内蒙古高校科学研究重点项目(NJZZ19209)。
关键词
调和函数
SALAGEAN算子
系数不等式
极值点
偏差
harmonic functions
Salagean operator
coefficient inequality
extreme points
distortion bounds