Document Type: Research Paper
Authors
Department of Mathematics, Payame Noor University, I. R. of Iran.
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\{f\in \mathcal{A}:\mathfrak{Re}\left( 1+\frac{zf^{\prime \prime }(z)}{f^{\prime }(z)}\right) <1+\frac{\alpha }{2},\quad 0<\alpha\leq1\right\}, \end{equation*} and \begin{equation*} \mathcal{F}(\alpha):=\left\{f\in \mathcal{A}:\mathfrak{Re}\left( 1+\frac{zf^{\prime \prime }(z)}{f^{\prime }(z)}\right) >\frac{1 }{2}-\mu,\quad -1/2<\mu\leq 1\right\}, \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.
Keywords
Main Subjects
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