一类单叶调和函数的系数不等式和极值点

Coefficient Inequalities and Extreme Points of a Class of Univalent Harmonic Functions

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.