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On T-neighborhoods of various classes of analytic functions | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 19 مرداد 1404 اصل مقاله (339.18 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.35301.5270 | ||
| نویسنده | ||
| Nassireh Ghaderi* | ||
| Department of Mathematics, Faculty of Science, Farhangian University, Sanandaj, Iran | ||
| تاریخ دریافت: 31 شهریور 1403، تاریخ بازنگری: 17 اسفند 1403، تاریخ پذیرش: 28 اسفند 1403 | ||
| چکیده | ||
| Let $\mathcal A$ be the class of analytic functions $f$ in the open unit disk ${\mathbb U}=\{z:\ |z|<1\}$ with the normalization conditions $f(0)=0$, $f'(0)=1.$ If $f(z) = z+ \sum_{n=2}^{\infty} a_n z^n$ and $\delta > 0$ are given, then the $T_\delta$-neighborhood of the function $f $ is defined as $$TN_\delta (f) = \left\{g(z)= z+ \sum_{n=2}^{\infty} b_n z^n \in \mathcal{ A} : \sum_{n=2}^{\infty} T_n\left|a_n - b_n\right| \leq \delta \right\},$$ where $T= \left\{T_n\right\}_{n=2}^{\infty}$ is a sequence of positive numbers. In the present paper we investigate some problems concerning $T_{\delta}-$neighborhoods of analytic functions with $T = \left\{\frac{n^2}{3^n n!}\right\}_{n=2}^{\infty}$. One of the considered problems is to find a number $\delta^\ast_T(A, B)$ such that $$\delta^\ast_T(A, B)= \inf \left\{\delta >0 : B \subset TN_\delta(f) \: \textnormal{for all} \: f \in \mathcal A\right\},$$ where the sets $A,B \in \mathcal A$ are given. | ||
| کلیدواژه‌ها | ||
| analytic functions؛ univalent functions؛ univalent؛ starlike؛ convex؛ close-to-convex؛ concave functions؛ $T_\delta-$neighborhood؛ $T-$factor | ||
| مراجع | ||
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