IJPAM: Volume 60, No. 3 (2010)

ON CERTAIN SUBCLASS OF
MULTIVALENT STARLIKE FUNCTIONS

F. Ghanim$^1$, M. Darus$^2$
$^1$Faculty of Management
Multimedia University
Selangor Darul Ehsan, Cyberjaya, 63100, MALAYSIA
e-mail: firas.ghanim@mmu.edu.my
$^2$School of Mathematical Sciences
Faculty of Science and Technology
University Kebangsaan Malaysia
(National University of Malaysia)
Selangor Darul Ehsan, Bangi, 43600, MALAYSIA
e-mail: maslina@ukm.my


Abstract.The object of the present paper is to introduce two interesting subclasses $T^* (p, \alpha ,\beta ,\gamma, A )$ and $C (p, \alpha ,\beta ,\gamma, A )$ of $p$-valent starlike functions in the open unit disc $U =\left\{ {z:\left\vert z \right\vert < 1} \right\}$ and prove various coefficient inequalities and distortion theorems for functions belonging to these subclasses. The radii of convexity for functions belonging to the classes $T^* (p, \alpha ,\beta ,\gamma, A )$ and $C (p, \alpha ,\beta ,\gamma, A )$ are also determined.

Received: March 5, 2010

AMS Subject Classification: 30C45

Key Words and Phrases: $p$-valent, starlike, convex, distortion theorems

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 3