Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682212120210501New subclass of analytic functions defined by subordination847855494010.22075/ijnaa.2018.13582.1706ENHosseinNaraghiDepartment of Mathematics, Payame Noor University, Tehran, IranParvanehNajmadiDepartment of Mathematics, Payame Noor University, Tehran, Iran0000-0001-6510-2647BahmanTaherkhaniDepartment of Mathematics, Payame Noor University, Tehran, IranJournal Article20180102By using the subordination relation $"\prec"$, we introduce an interesting subclass of analytic functions as follows:<br />\begin{equation*}<br />\mathcal{S}^*_{\alpha}:=\left\{f\in \mathcal{A}:\frac{zf'(z)}{f(z)}\prec \frac{1}{(1-z)^\alpha},\ \ |z|<1\right\},<br />\end{equation*}<br />where $0<\alpha\leq1$ and $\mathcal{A}$ denotes the class of analytic and normalized functions in the unit disk $|z|<1$. In the present paper, by the class $\mathcal{S}^*_{\alpha}$ and by the Nunokawa lemma we generalize a famous result connected to starlike functions of order $1/2$. Also, coefficients inequality and logarithmic coefficients inequality for functions of the class $\mathcal{S}^*_{\alpha}$ are obtained.https://ijnaa.semnan.ac.ir/article_4940_a768d0ff6e35a2d3a84f5ec180873130.pdf