和一类积分算子相关的单叶函数的子类  

Subclasses of Univalent Functions Associated with Integral Operators

作　　者：殷建连[1] 

机构地区：[1]淮阴师范学院,江苏淮阴223300

出　　处：《大学数学》2010年第6期89-92,共4页College Mathematics

摘　　要：在Ruscheweyh定义了解析函数的Ruscheweyh导数[1]之后,许多学者相继研究了与Ruscheweyh导数有关的单叶或者多叶解析函数类.近来,Jung,Ki m和Srivastava[5]引入了下面的单参数积分算子类:Iσf(z)=zΓ2(σσ)∫0zlogtzσ-1f(t)dt,σ>0,f∈Α.算子Iσ和Flett[6]研究的乘数变换密切相关.本文利用算子Iσ定义了两个函数类.首先研究在单位圆内解析的单叶函数类Rσ(A,B),给出函数类的包含关系Rσ(A,B)Rσ+1(A,B),同时也考虑了在积分算子Fλ的作用下的函数类的包含关系以及当λ取特殊值1时的特殊情况.其次研究了函数类Rσ(A,B)中系数为正实数的函数类Sσ(A,B),给出函数f(z)属于类Sσ(A,B)的充分必要条件.Since defined Ruscheweyh derivatives of analytic functions by Ruscheweyh[1],many scholars have studied classes of univalent or multivalent analytic functions associated with Ruscheweyh derivatives（[2-4]）.Recently,Jung,Kim and Srivastava introduced the following one-parameter family of integral operator： I^σf（z）=2^σ/zΓ（σ）∫0^z（logz/t）^σ-1f（t）dt,σ〉0,f∈Α.The operatorIσ is closely related to the multiplier transformations studied by Flett[6].In this article,making use of operator Iσ,two subclasses are introduced.Firstly,subclasses Rσ（A,B） is introduced in the open unit disk,the inclusion relation of Rσ（A,B）belong to Rσ＋1（A,B） is obtained.Some properties of class Rσ（A,B） are preserved in connection with the operator Fλ and some condusions are acquired according to the special parameter λ=1.Secondly,class Sσ（A,B） of analytic functions belonging to Rσ（A,B） with the positive coefficients is investigated,the necessary and sufficient condition of f（z） falling into Sσ（A,B） is obtained.

关 键 词：单叶解析函数 积分算子 子类 充分必要条件 

分 类 号：O174.5[理学—数学]