分数次微积分算子在一类解析函数上的应用  

Application of Fractional Calculus on Certain Subclass of Analytic Functions

作　　者：韦叶[1] 

机构地区：[1]淮海工学院数理科学系,江苏连云港222005

出　　处：《淮海工学院学报（自然科学版）》2007年第3期6-9,共4页Journal of Huaihai Institute of Technology:Natural Sciences Edition

基　　金：江苏省高校自然科学基金资助项目(04KJB110154)

摘　　要：基于不同的算子,某些p叶解析函数类的性质和特征已被广泛研究.用Hadamard积(或卷积)定义积分算子In+p,并利用算子In+p与微分从属关系定义了p叶解析函数类Tn+p(η;A,B),给出函数f(z)属于类Tn+p(η;A,B)的充分必要条件,考虑类Tn+p(η;A,B)中的函数在u阶分数次微积分算子作用下的准确的偏差定理.Based on different operators, some properties and characters of p-valent analytic functions have been investigated extensively. A certain integral operator In＋p is defined by convolution or Hadamard product. Making use of operator In＋p and differential subordnation, the author introduces the subclass Tn＋p（η;A,B）, abtaining the necessary and sufficient condition of f（z） belonging to Tn＋p（η;A,B）. Using fractional calculus operators of order u, he gets the precise distortion theorems of analytic functions, which belong to class Tn＋p （η;A,B）.

关 键 词：P叶解析函数 微分从属 分数次微积分算子 

分 类 号：O174.51[理学—数学]