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Certain differential superordinations using a multiplier transformation and Ruscheweyh derivative
Authors: Alina Alb Lupaş
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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 $IR_{\lambda ,l}^{m}$.Department of Mathematics and Computer Science
University of Oradea
1 Universitatii Street, 410087 Oradea, Romania
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University of Oradea
1 Universitatii Street, 410087 Oradea, Romania
E-mail:
Fulltext
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Contents
- Academician Mitrofan M. Choban founder of the moldavian scientific school in topology
- Liouville's theorem for vector-valued functions
- On the number of metrizable group topologies on countable groups
- Short signatures from the difficulty of factoring problem
- Selected Old Open Problems in General Topology
- Infinitely many maximal primitive positive clones in a diagonalizable algebra
- Functional compactifications of T0-spaces and bitopological structures
- On free groups in classes of groups with topologies
- On a four-dimensional hyperbolic manifold with finite volume
- On spaces of densely continuous forms
- A selection theorem for set-valued maps into normally supercompact spaces
- Minimal m-handle decomposition of three-dimensional handlebodies
- Examples of quasitopological groups
- Certain differential superordinations using a multiplier transformation and Ruscheweyh derivative
- The 20th Conference on Applied and Industrial Mathematics (CAIM-2012) dedicated to the 70th anniversary of Academician Mitrofan M. Choban
