Generalization properties of Bernardi integral operator

Year 2025, Volume: 74 Issue: 3, 364 - 374, 23.09.2025

Muhammet Kamali , Hatun Özlem Guney , Shigeyoshi Owa

https://doi.org/10.31801/cfsuasmas.1521845

https://izlik.org/JA84FY32LN

Abstract

Let $A\left( n\right)$ be the class of analytic functions $f\left(z\right)$ of the form
\begin{equation*}
f\left( z\right) =z+\sum_{k=n}^{\infty }a_{k}z^{k},\;\;\left(
n=2,3,4,...\right)
\end{equation*}
in the open unit disk $U.$ We introduce the integral operator $B_{j}f\left(
z\right) $$=B\left( B_{j-1}f\left( z\right) \right) $, $B_{1}f\left(
z\right) =Bf\left( z\right)$ and $B_{0}f\left( z\right) =f\left( z\right) $. In the present paper, we define the subclass $M_{j}\left( n,\gamma ,\alpha
\right) $ and discuss some interesting properties of $f\left( z\right) \in
A\left( n\right)$ concerning with the class $M_{j}\left( n,\gamma ,\alpha
\right) .$

Keywords

Analytic function , Bernardi integral operator , coefficient problem , argument problem , subordination

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