Applications of a Multiplier Transformation and Ruscheweyh Derivative for Obtaining New Strong Differential Subordinations

Symmetry

Alina Alb Lupaş¹ 

[1] Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania;

关键词: strong differential subordination;    univalent function;    convex function;    best dominant;    extended differential operator;    convolution product;   

DOI  :  10.3390/sym13081312

来源: DOAJ

【 摘 要 】

Here, we study strong differential subordinations for the extended new operator $I{R}_{\lambda ,l}^m$ defined by the Hadamard product of the extended multiplier transformation $I\left(m,\lambda ,l\right)$ and the extended Ruscheweyh derivative $R^m$, on the class of normalized analytic functions ${\mathcal{A}}_{n\zeta }^{\ast }=\{f\in \mathcal{H}(U\times \overline{U}),f(z,\zeta )=z+a_{n+1}\left(\zeta \right)z^{n+1}+\cdots ,z\in U,$$\zeta \in \overline{U}\}$, by $I{R}_{\lambda ,l}^m:{\mathcal{A}}_{n\zeta }^{\ast }\to {\mathcal{A}}_{n\zeta }^{\ast }$, $I{R}_{\lambda ,l}^{m}f\left(z,\zeta \right)=\left(I\left(m,\lambda ,l\right)\ast R^m\right)f\left(z,\zeta \right).$

【 授权许可】

Unknown