基于Lp(a,c)算子定义的亚纯函数邻域的性质

摘要

令∑p表示形如f(z) =z-p+∑()n=1anzn-p且在空心单位圆盘E=｛z∶0＜｜z｜＜1｝内解析的p叶函数全体组成的函数类.利用线性算子Lp(a,c)定义亚纯多叶函数的新子类Ωp(a,c;A,B)和Ω+p(a,c;A,B)的基础上,延伸了亚纯函数的邻域概念,讨论了亚纯函数的邻域与函数新子类的包含关系和相关性质.%Let ∑p be the class of functions f(z) = z-p + ∞∑n=1 αnzn-p analytic in the punctured unit disk ofE = {z:0 <| z| < 1}. Making use of a linear operator Lp(α,c) , a new subclass Ωp(α,c;A,B) and Ωp+(α,c; A,B) based on the meromorphic multivalent functions is defined. The concept of neighborhoods about meromorphic multivalent functions is extended. Properties of subordination and related properties are discussed between the neighborhood of meromorphic multivalent function and new subclass of functions.