推广的Libera积分算子对S(α,β)类函数的运算

CALCULATION OF SPREADING LIBERA INTEGAL OPERATOR TO S(α, β) FUNCTION

我们用S(α,β)表示在单位圆E={z∶|z+<1}内解析并且满足条件|[zf′(z)/f(z)-1]/[αzf′(z)/f(z)+1]|<β,0≤α≤1,0<β≤1,的函数之全体,在本文中,将证明如果函数f(z)属于S(α,β),那么F_c(f)=((C+1)/z^c) integral from n=0 to 1 t^(c-1)f(t)dt也属于S(α,β)。

L(?)t S(α, β) denote all the functions analytic in the unit disc E={z∶|z|<1} satisfying the condition.|(zf'(z)/f(z)-1)/(αzf'(z)/f(z))|<β 0≤α≤1, 0≤β≤1in this paper, it is proved that if f(z) belongs to S(α, β), the function F_(?)(f)=(C+1/z) integral from n=0 to z t^(c-1)f(t)dt also belongs to S(α, β)