The $n$-valent convexity of Frasin integral operators
UDC 517.5 Let $ f_{i},$ $i\in\lbrace 1,2,\ldots, k\rbrace,$ is an analytic function on the unit disk in the complex plane of the form$f_{i}(z) = z^{n} + a_{i,n+1}z^{n+1} + \ldots, n\in\mathbb{N} = \lbrace 1,2,\ldots\rbrace.$We consider the Frasin integral operator as follows:\begin{gather*}\label{e1...
Збережено в:
| Дата: | 2021 |
|---|---|
| Автори: | , , , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2021
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/88 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 517.5
Let $ f_{i},$ $i\in\lbrace 1,2,\ldots, k\rbrace,$ is an analytic function on the unit disk in the complex plane of the form$f_{i}(z) = z^{n} + a_{i,n+1}z^{n+1} + \ldots, n\in\mathbb{N} = \lbrace 1,2,\ldots\rbrace.$We consider the Frasin integral operator as follows:\begin{gather*}\label{e1.3}G_{n}(z)=\int\limits_{0}^{z} n\xi^{(n-1)}\bigg(\dfrac{f'_{1}(\xi)}{n\xi^{n-1}}\bigg)^{\alpha_{1}}\cdots\bigg(\dfrac{f'_{k}(\xi)}{n\xi^{n-1}}\bigg)^{\alpha_{k}}d\xi.\end{gather*}In this paper, we obtain a sufficient condition under which this integral operator is $n$-valent convex and get other interesting results.
  |
|---|---|
| DOI: | 10.37863/umzh.v73i2.88 |