算子I_n在解析函数上的应用

Some Applications of the I_n Operator in Analytic Functions

定义了算子In:Inf=f(-1)n*f=[z/(1-z)n+1](-1)*f利用算子In刻画了4个函数类的新子类,证明了:S*n(γ)S*n+1(γ),Cn(γ)Cn+1(γ),Kn(β,γ)Kn+1(β,γ),K*n(β,γ)K*n+1(β,γ).

In this paper, operator In is defined as In：Inf=f（-1）n＊f=[z/（1-z）n＋1]（-1）＊f Then taking advantage of operator In, the new subclasses of the above-mentioned 4 classes are characterized. The following relations of these subclasses are proved： S＊n（γ）S＊n＋1（γ）,Cn（γ）Cn＋1（γ）,Kn（β,γ）Kn＋1（β,γ）,K＊n（β,γ）K＊n＋1（β,γ）.