Geodesic
Certain differential superordinations using a multiplier transformation and Ruscheweyh derivative
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2013), pp. 119-131 
Alina Alb Lupaş. Certain differential superordinations using a multiplier transformation and Ruscheweyh derivative. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2013), pp. 119-131. http://geodesic.mathdoc.fr/item/BASM_2013_2_a13/
@article{BASM_2013_2_a13,
     author = {Alina Alb Lupa\c{s}},
     title = {Certain differential superordinations using a~multiplier transformation and {Ruscheweyh} derivative},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {119--131},
     year = {2013},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2013_2_a13/}
}
TY  - JOUR
AU  - Alina Alb Lupaş
TI  - Certain differential superordinations using a multiplier transformation and Ruscheweyh derivative
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2013
SP  - 119
EP  - 131
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/BASM_2013_2_a13/
LA  - en
ID  - BASM_2013_2_a13
ER  - 
%0 Journal Article
%A Alina Alb Lupaş
%T Certain differential superordinations using a multiplier transformation and Ruscheweyh derivative
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2013
%P 119-131
%N 2
%U http://geodesic.mathdoc.fr/item/BASM_2013_2_a13/
%G en
%F BASM_2013_2_a13

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $IR_{\lambda,l}^m\colon\mathcal A\to\mathcal A$, $IR_{\lambda,l}^m(z):=(I(m,\lambda,l)\ast R^m)f(z)$, where $\mathcal A_n=\{f\in\mathcal H(U)\colon f(z)=z+a_{n+1}z^{n+1}+\dots,\ z\in U\}$ is the class of normalized analytic functions, with $\mathcal A_1=\mathcal A$. We study some differential superordinations regarding the operator $IR_{\lambda,l}^m$.

[1] Alb Lupaş A., “Certain differential subordinations using Salagean and Ruscheweyh operators”, Acta Universitatis Apulensis, 29 (2012), 125–129 | MR | Zbl

[2] Alb Lupaş A., “Certain differential subordinations using a generalized Salagean operator and Ruscheweyh operator”, Journal of Mathematics and Applications, 33 (2010), 67–72 | MR

[3] Alb Lupaş Alina, “A note on a certain subclass of analytic functions defined by multiplier transformation”, Journal of Computational Analysis and Applications, 12:1-B (2010), 369–373 | MR | Zbl

[4] Alb Lupaş Alina, “Certain differential superordinations using Sălăgean and Ruscheweyh operators”, Analele Universităţii din Oradea, Fascicola Matematica, 17:2 (2010), 203–210 | MR

[5] Alb Lupaş Alina, “Certain differential superordinations using a generalized Sălăgean and Ruscheweyh operators”, Acta Universitatis Apulensis, 25 (2011), 31–40 | MR | Zbl

[6] Al-Oboudi F. M., “On univalent functions defined by a generalized Sălăgean operator”, Ind. J. Math. Math. Sci., 25 (2004), 1429–1436 | DOI | MR | Zbl

[7] Cătaş A., “On certain class of $p$-valent functions defined by new multiplier transformations”, Proceedings Book of the International Symposium on Geometric Function Theory and Applications (August 20–24, 2007, TC Istanbul Kultur University, Turkey), 241–250

[8] Miller S. S., Mocanu P. T., “Subordinants of Differential Superordinations”, Complex Variables, 48:10 (2003), 815–826 | DOI | MR | Zbl

[9] Ruscheweyh St., “New criteria for univalent functions”, Proc. Amer. Math. Soc., 49 (1975), 109–115 | DOI | MR | Zbl

[10] Sălăgean G. St., “Subclasses of univalent functions”, Lecture Notes in Math., 1013, Springer Verlag, Berlin, 1983, 362–372 | DOI | MR