函数族S（α，n）的推广  

Extension of Function Class S (α, n)

作　　者：蒋润荣[1] 

机构地区：[1]广西民族学院数学系

出　　处：《广西民族大学学报（自然科学版）》1995年第1期11-14,共4页Journal of Guangxi Minzu University ：Natural Science Edition

摘　　要：设Ａ（ｎ）为标准化的解析函数ｆ（ｚ）＝ｚ＋ａｎｚｎ＋…（ｎ≥２，｜Ｚ｜＜１）的族，又设Ｓ（α，β，ｎ）表示Ａ（ｎ）中满足条件Ｒｅ｛（１－β）ｆ（ｚ）／Ｚ＋βｆ′（ｚ）｝＞α的全体函数ｆ（Ｚ）所构成的族，其中β≥０，０≤α＜１．当β＝０时，族ｓ（α，β，ｎ）化为族ｓ（α，ｎ）［１］，本文得到了ｓ（α，β，ｎ）中函数的积分表示式、系数估计和变形定理，并且这些结果是［１］和［２］中相应结果的推广．Let A(n) be the class of normalized andlytic function f(z)=Z+anZn+... (n≥2. |Z|< 1). Let S (a. β, n) denote all functions satisfying condition Re{(1-b)f (Z)/Z+βf' (Z)}>a in A (n).where β≥0. 0≤a<1. When β=0, the class S (a. β. n) becomes class s(a, n) [1] . This paper obtain that the representation formulas by intergration. estimation of coefficients and distortion theorem with repect to functions in the class S (a. β. n). These results are also the extension of well-know results in [1]and [2].

关 键 词：正实部函数 单叶半径 变形定理 系数估计 极值函数 星象半径 

分 类 号：O174[理学—数学]