关于p-叶星形性和强星形性的充分条件 (英)

On Sufficient Conditions for p-Valently Starlikeness and Strong Starlikness

中文关键词:  解析函数  星形函数  强星形函数  从属.

英文关键词:analytic function  starlikeness  strongly starlikeness  subordination.

中文摘要:

      本文利用微分从属的方法得到了单位圆盘内p-叶星形函数和强星形函数的某些充分条件.

英文摘要:

      Let $A_{n}(p)~(p,n\in N=\{1,2,3,\cdots\})$ denote the class of functions of the form $f(z)=z^{p}+a_{p+n}z^{p+n}+\cdots$ that are analytic in the unit disk $E=\{z:|z|<1\}$. By using the method of differential subordinations we give some sufficient conditions for a function $f(z)\in A_{n}(p)$ to be $p$-valently starlike or strong starlike.