亚纯p叶函数的子类

ON SUBCLASSES OF MEROMORPHIC p-VALENT FUNCTIONS

设G_((?),p)(α)是0<|z|<1内解析函数f(z)=^(-p)+α_(1-p)z^(1-p)+…组成的类,f(z)满足 这里0<α≤1,p是正整数,n是大于—p的任一整数,本文证明G_((?)+1,p)(α)是G_((?),p)(α)的子类,从而类中函数是亚纯P叶星形的;进而研究G_((?),p)(α)中函数的积分。

Let Gn,p(α)be class of functions f(z) = z -p + a1-pZ1-9 + …which are analytic in 0 < |z| < 1 and satisfywhere 0 < α ≤ 1 ,p is a positive integer and in n is any integer greater than - p. It is proved that Gn+l.p(α) (?) Gn,p(α), and hence all functions in Gn,p(α) are mermorphically p-valent starlike. Further integrals of functions in Gn,p(α) are studied.