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New subclasses of Ozaka's convex functions | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 16، دوره 14، شماره 3، خرداد 2023، صفحه 189-199 اصل مقاله (417.28 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.28231.4081 | ||
| نویسنده | ||
| Mohammad Ali Abolfathi* | ||
| Department of Mathematics, Faculty of Sciences, Urmia University, P. O. Box 165, Urmia, Iran | ||
| تاریخ دریافت: 27 تیر 1401، تاریخ بازنگری: 09 خرداد 1401، تاریخ پذیرش: 20 مهر 1401 | ||
| چکیده | ||
| Let $\mathcal{S}^{\ast}_{L}(\uplambda)$ and $\mathcal{CV}_L(\uplambda)$ be the classes of functions $f$, analytic in the unit disc $\Updelta=\{z\colon|z|<1\}$, with the normalization $f(0)=f'(0)-1=0$, which satisfies the conditions \begin{equation*} \frac{zf'(z)}{f(z)}\prec \left(1+z\right)^{\uplambda}\quad\text{and}\quad \left(1+\frac{zf''(z)}{f'(z)}\right)\prec \left(1+z\right)^{\uplambda} \qquad \left(0<\uplambda\le 1 \right), \end{equation*} where $\prec$ is the subordination relation, respectively. The classes $\mathcal{S}^{\ast}_{L}(\uplambda)$ and $\mathcal{CV}_L(\uplambda)$ are subfamilies of the known classes of strongly starlike and convex functions of order $\uplambda$. We consider the relations between $\mathcal{S}^{\ast}_{L}(\uplambda)$, $\mathcal{CV}_L(\uplambda)$ and other classes geometrically defined. Also, we obtain the sharp radius of convexity for functions belonging to $\mathcal{S}^{\ast}_{L}(\uplambda)$ class. Furthermore, the norm of pre-Schwarzian derivatives and univalency of functions $f$ which satisfy the condition \begin{equation*} \Re\left\{1+\frac{zf''(z)}{f'(z)}\right\}<1+\frac{\uplambda}{2}\qquad \myp{z \in \Updelta}, \end{equation*} are considered. | ||
| کلیدواژهها | ||
| Univalent functions؛ Subordination؛ Strongly starlike functions؛ Domain bounded by Sinusoidal spiral | ||
| مراجع | ||
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