OZAKI'S CONDITIONS FOR GENERAL INTEGRAL OPERATOR

Abstract

Assume that $mathbb{D}$ is the open unit disk. Applying Ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{G}(alpha)$ and $mathcal{F}(mu)$ as follows begin{equation*} mathcal{G}(alpha):=left{fin mathcal{A}:mathfrak{Re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right) frac{1 }{2}-mu,quad -1/2<muleq 1right}, end{equation*} respectively, where $z in mathbb{D}$. In this paper, we study the mapping properties of this classes under general integral operator. We also, obtain some conditions for integral operator to be convex or starlike function.