算子在解析函数上的应用  

The Applications of Operator Dα on Analytic Functions

作　　者：华芳[1] 

机构地区：[1]镇江高等专科学校教师教育系,江苏丹阳212310

出　　处：《泰州职业技术学院学报》2007年第3期71-74,共4页Journal of Taizhou Polytechnic College

摘　　要：用A表示在E=｛z│z│1｝内解析,具有形式f(z)=z+(∞∑n=2)anzn的全体函数组成的类。当f∈A时,记S*(γ),C(γ),K(β,γ),K*(β,γ)为γ阶星象函数,γ阶凸象函数,γ型β阶近于凸函数,γ型β阶拟凸函数类,0≤β<1,0≤γ<1。用算子Dα刻划上述四个函数类的新子类Sα*(γ),Cα(γ),Kα(β,γ),Kα*(β,γ)建立了包含关系。Let A denote the class of analytic functions in E=（z： ｜z｜〈1 ）and these functions can be described as f（z）=z＋^∞∑n=2 anzn when f∈A , let S^＊（γ）,C（γ）,K（β,γ）,K^＊（β,γ） represent the familiar subclasses of A. such subclasses are consisted of functions which are starlike of order α in E, convex of order α in E, close-to-convex of ordex β and type γ in E, quasi-convex of order β and type γ in E, strongly starlike of order β and type γ in E, and strongly convex of order β and type γ in E,respectively, 0 ≤β〈1, and 0≤γ〈1. In this paper we introduce and study some new classes of analytic functions defined by operator D^α Inclusion relations are established.

关 键 词：解析函数 星象函数 凸象函数 近于凸函数 拟凸函数 

分 类 号：O17[理学—数学]