پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 675 |
| تعداد مقالات | 9,837 |
| تعداد مشاهده مقاله | 69,873,561 |
| تعداد دریافت فایل اصل مقاله | 49,202,921 |
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 | ||
|
[1] F.G. Avkhadiev, Ch. Pommerenke, and K.J. Wirths, On the coefficients of concave univalent functions, Math. Nachr. 271 (2004), 3–9. [2] F.G. Avkhadiev, Ch. Pommerenke and K.-J. Wirths, Sharp inequalities for the coefficients of concave Schlicht functions, Comment. Math. Helv. 81 (2006), 801–807. [3] F.G. Avkhadiev and K.J. Wirths, Convex holes produce lower bound for coefficients, Complex Var. Theory Appl. 47 (2002), no. 7, 553–563. [4] U. Bednarz, Stability of the Hadamard product of k-uniformly convex and k-starlike functions in certain neighbourhood, Demonstr. Math. 38 (2005), no. 4, 837–845. [5] U. Bednarz and S. Kanas, Stability of the integral convolution of k-uniformly convex and k-starlike functions, J. Appl. Anal. 10 (2004), no. 1, 105–115. [6] U. Bednarz and J. Sokól, On the integral convolution of certain classes of analytic functions, Taiwanese J. Math. 13 (2009), no. 5, 1387–1396. [7] U. Bednarz and J. Sokol, T-neighborhoods of analytic functions, J. Math. Appl. 32 (2010), 25–32. [8] A. Bielecki and Z. Lewandowski, Sur une generalisation de quelques theoremes de M. Biernacki sur les fonctions analytiques, Ann. Polon. Math. 12 (1962), 65–70. [9] P.L. Duren, Univalent Functions, Springer Verlag, Grund. Math. Wiss. 259, New York, Berlin, Heidelberg, Tokyo, 1983. [10] R. Fournier, A note on neighbourhoods of univalent functions, Proc. Amer. Math. Soc. 87 (1983), no. 1, 117–120. [11] R. Fournier, On neighbourhoods of univalent starlike functions, Ann. Polon. Math. 47 (1986), no. 20, 189–202. [12] R. Fournier, On neighbourhoods of univalent convex functions, Rocky Mountain J. Math. 16 (1986), no. 3, 579–589. [13] L. Lewin, Dilogarithms and Associated Functions, Macdonald, London, 1958. [14] St. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81 (1981), no. 4, 521–527. [15] S. Shams and S.R. Kulkarni, Certain properties of the class of univalent functions defined by Ruscheweyh derivative, Bull. Cal. Math. Soc. 97 (2005), no. 3, 223–234. [16] S. Shams, A. Ebadian, M. Sayadiazar, and J. Sokol, T-neighborhoods in various classes of analytic functions, Bull. Korean Math. Soc. 51 (2014), no. 3, 659–666. [17] T. Sheil-Small, On linear accessibility and the conformal mapping of convex domains, J. Anal. Math. 25 (1972), 259–276. [18] T. Sheil-Small and E. M. Silvia, Neighborhoods of analytic functions, J. Anal. Math. 52 (1989), 210–240. [19] J. Stankiewicz, Neighbourhoods of meromorphic functions and Hadamard products, Ann. Polon. Math. 46 (1985), 317–331 | ||
|
آمار تعداد مشاهده مقاله: 95 تعداد دریافت فایل اصل مقاله: 229 |
||