Some properties of Noor integral operator of $(n+p-1)$-th order

Abstract

Let $A(p)$ be the class of functions $f(z)=z^{p}+\sum_{k=p+1}^{ınfty}a_{k}z^{k}$ $(pın N=\{1,2,\dots\})$ which are analytic in the unitdisc $U=\{z:|z|<1\}$. The object of the present paper is to give some properties of Noor integral operator $I_{n+p-1}f(z)$ of $(n+p-1)$-th order,where $I_{n+p-1}f(z)=\left[ \frac{z^{p}}{(1-z)^{n+p}}\right]^{(-1)}*f(z)$ $(n>-p$, $f(z)ın A(p))$ and $*$ denotes convolution (Hadamard product).