Certain differential superordinations using a~multiplier transformation and Ruscheweyh derivative

Alina Alb Lupaş

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2013), pp. 119-131.

Résumé

In the present paper we define a new operator, by means of convolution product between Ruscheweyh derivative and the multiplier transformation $I(m,\lambda ,l)$. For functions $f$ belonging to the class $\mathcal{A}$ we define the differential operator $I{R}_{\lambda ,l}^m:\mathcal{A}\to \mathcal{A}$, $I{R}_{\lambda ,l}^m(z):=(I(m,\lambda ,l)\ast R^m)f(z)$, 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 $I{R}_{\lambda ,l}^m$.

Bibliographie

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