用线性算子定义的亚纯p叶函数类

Subclasses of meromorphically p-valent functions defined by linear operator

利用线性算子Dα定义了亚纯多叶函数的新子类Tp,α(;βA,B)和Tp+,α(;βA,B),将解析函数的邻域概念应用到亚纯多叶函数上,探讨了这两个函数类的性质,得到函数f(z)=z-p+∑∞n=1anzn-p在类Tp,α(;βA,B)中的充分条件,并由此研究了其他性质.利用类Tp+,α(;βA,B)的定义得到了f(z)=-z p+∑n∞=p an zn在类Tp+,α(;βA,B)中的充要条件.

In this paper, two new subclasses of meromorphic multivalent functions are defined by a limear operator, and the familiar concept of neighborhoods of analytic functions is applied to meromorphic multivalent functions. The properties of the classes are investigated by using the concept of neighborhoods. The sufficient condition for function given by f（z）=z^-p＋∑n=1^∞,anz^n-p belonging to the class Tp,a（β;A,B） is derived, and the sufficient and necessary condition for the function given by f（z）=z^-p＋∑n=p^∞｜ap｜z^n in the class Tp,a^＋（β;A,B） is studied with the use of the definition of the class Tp,a^＋（β;A,B）.