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IMI/Publicaţii/BASM/Ediţii/BASM n.2 (72) -n.3 (73), 2013/

Certain differential superordinations using a multiplier transformation and Ruscheweyh derivative

Authors: Alina Alb Lupaş

Abstract

In the present paper we define a new operator, by means of convolution product between Ruscheweyh derivative and\ the multiplier transformation $% I\left( m,\lambda ,l\right) $. For functions $f$ belonging to the class $% \mathcal{A}$ we define the differential operator $IR_{\lambda ,l}^{m}:% \mathcal{A}\rightarrow \mathcal{A}$, $IR_{\lambda ,l}^{m}f\left( z\right) :=\left( I\left( m,\lambda ,l\right) \ast R^{m}\right) f\left( z\right) ,$ where $\mathcal{A}_{n}=\{f\in \mathcal{H}(U):\ f(z)=z+a_{n+1}z^{n+1}+\dots ,\ z\in U\}$\ is the class of normalized analytic functions, with $\mathcal{A% }_{1}=\mathcal{A}.$ We study some differential superordinations regarding the operator $IR_{\lambda ,l}^{m}$.

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