星形函数族的一个子族的极值点与支撑点(英文)

THE EXTREME POINTS AND SUPPORT POINTS OF A SUBCLASS OF STARLIKE FUNCTIONS

设Ｆ（｛ｎ｝）＝｛ｆ（ｚ）：ｆ（ｚ）在｜ｚ｜＜１内解析，ｆ（ｚ）＝ｚ－∞ｎ＝１ａｎｚｎ，ａｎ≥０，＋∞ｎ＝２ｎａｎ≤１｝，则Ｆ（｛ｎ｝）是星形函数族的一个子族．许多学者研究了这个函数族．设Ｍ＝｛ｆ（ｚ）：ｆ（ｚ）在｜ｚ｜＜１内解析，ｆ（ｚ）＝ｚ－∞ｎ＝１ａｎｚｎ，ａｎ≥ａｎ＋１≥０，＋∞ｎ＝２ｎａｎ≤１｝．在本文中我们找出了函数族Ｍ的极值点与支撑点．

Let F({n})={f(z): f(z) is analytic in |z|<1, f(z)=z-+∞n=2a nz n, a n≥0, +∞n=2na n≤1}. It is well known that F({n}) is a subclass of starlikeness of functions. This family has been studied by many people. LetM={f(z): f(z)=z-∞n=2a nz n, a n≥a n+1 ≥0, ∞n=2na n≤1}. In this chapter we obtained the extreme points and support points of M.