The $n$-valent convexity of Frasin integral operators

  • R. Khani Payame Noor Univ., Tehra
  • Sh. Najafzadeh Payame Noor Univ., Tehran, Iran
  • A. Ebadian Payame Noor Univ., Tehran, Iran
  • I. Nikoufar Payame Noor Univ., Tehran, Iran


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:
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.
In this paper, we obtain a sufficient condition under which this integral operator is $n$-valent convex and get other interesting results.



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How to Cite
Khani , R., S. Najafzadeh, A. Ebadian, and I. Nikoufar. “ The $n$-Valent Convexity of Frasin Integral Operators”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 2, Feb. 2021, pp. 278 -2, doi:10.37863/umzh.v73i2.88.
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