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New subclass of analytic functions defined by subordination | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 68، دوره 12، شماره 1، مرداد 2021، صفحه 847-855 اصل مقاله (599.85 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2018.13582.1706 | ||
| نویسندگان | ||
| Hossein Naraghi؛ Parvaneh Najmadi* ؛ Bahman Taherkhani | ||
| Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| تاریخ دریافت: 12 دی 1396، تاریخ بازنگری: 08 تیر 1397، تاریخ پذیرش: 08 تیر 1397 | ||
| چکیده | ||
| By using the subordination relation $"\prec"$, we introduce an interesting subclass of analytic functions as follows: \begin{equation*} \mathcal{S}^*_{\alpha}:=\left\{f\in \mathcal{A}:\frac{zf'(z)}{f(z)}\prec \frac{1}{(1-z)^\alpha},\ \ |z|<1\right\}, \end{equation*} 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. | ||
| کلیدواژهها | ||
| univalent؛ subordination؛ starlike functions؛ coefficients estimates؛ logarithmic coefficients؛ Nunokawa's lemma | ||
| مراجع | ||
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