算子在解析函数上的应用

The Applications of Operator Dα on Analytic Functions

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.