IJPAM: Volume 34, No. 4 (2007)

CERTAIN APPLICATIONS OF DIFFERENTIAL
SUBORDINATION AND SUPERORDINATION

N. Marikkannan$^1$, P. Sooriyakala$^2$, C. Ganesamoorthy$^3$
$^1$Department of Applied Mathematics
Sri Venkateswara College of Engineering
Sriperumbudur, 602105, INDIA
e-mails: mari@svce.ac.in, natarajan.marikkannan@gmail.com
$^2$Department of Mathematics
Jaya College of Arts and Science
Thiruninravur, 602024, INDIA
e-mail: sooriya_kala@yahoo.com
$^3$Department of Mathematics
Alagappa University
Karaikudi, INDIA
e-mail: ganesamoorthyc@yahoo.com


Abstract.In the present investigation we obtain sufficient conditions for certain subclass of multivalent analytic functions defined on open unit disk to be subordinated and superordinated by convex univalent functions. As a special case of this we obtain results involving Ruscheweyh derivative, Salagean derivative, Carlson-Shaffer operator, Dziok-Srivastava operator and multiplied transformation.

Received: November 29, 2006

AMS Subject Classification: 30C45, 30C80

Key Words and Phrases: analytic functions, univalent functions, Hadamard producut, differential subordinations, differential superordinations, Ruscheweyh derivative, Salagean derivative, Carlson-Shaffer operator, Dziok-Srivastava linear operator, multiplier transformation.

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 4