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

Abstract

Let $A(p)$ be the class of functions $f(z)=z^p+\sum _{k=p+1}^{ınfty}{a}_k{z}^k$ $(pınN=\{1,2,\dots \})$ 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 $I_{n+p-1}f(z)={\left[\frac{z^p}{(1-z{)}^{n+p}}\right]}^{(-1)}\ast f(z)$ $(n>-p$, $f(z)ınA(p))$ and $\ast$ denotes convolution (Hadamard product).