摘要
本文利用Rusheweyh导数引进函数类T(α+p—1,β)={f(z)|f(z)∈A(p),Re(D^(α+p)f)/(D^(α+p-1)f>β}。当0≤β≤1/2时,证明了T(α+p,β)(?)T(α+p-1,β)。还讨论了由积分算子定义的函数F(z)=(p+c)·z^(-(?))integral from n=0 to z t^((?)-1)f(t)dt,(|z|<1)的映射性质。推广了某些文献中的一些结果。
This paper introduces a new class of functions by using Rusheweyh derivative—T (α+p—1,β), where p≥0,α+p≥0 ; proves that T(α+P,β)(?)T(α+p—1,β) when 0≤β≤1/2; and discuss some properties of the integral operator I(f)=F(z)=[(p+c)/z^c]integral from n=0 to z t^(0-1)f(t)dt. Our theorems generalize some known resuts.
关键词
P叶函数
星像函数
凸像函数
P-valent function
Hadamard product
starlike function
convex function
