@article {
author = {Kargar, Rahim and Ebadian, Ali},
title = {Ozaki's conditions for general integral operator},
journal = {Sahand Communications in Mathematical Analysis},
volume = {05},
number = {1},
pages = {61-67},
year = {2017},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2017.17786},
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 = {Starlike function,convex function,Locally univalent,Integral operator,Ozaki's conditions},
url = {https://scma.maragheh.ac.ir/article_17786.html},
eprint = {https://scma.maragheh.ac.ir/article_17786_7cc766b7af9e228a4c99a78217ebf0de.pdf}
}