IJPAM: Volume 61, No. 3 (2010)

NEW SUBCLASS OF MULTIVALENT
HYPERGEOMETRIC MEROMORPHIC FUNCTIONS

F. Ghanim$^1$, M. Darus$^2$
$^1$Faculty of Management
Multimedia University
Cyberjaya, 63100, Selangor D. Ehsan, MALAYSIA
e-mail: [email protected]
$^2$School of Mathematical Sciences
Faculty of Science and Technology
University Kebangsaan Malaysia
Bangi, 43600, Selangor D. Ehsan, MALAYSIA
e-mail: [email protected]


Abstract.In this paper, we introduce a new class $\Sigma_p^*\left({A,B,k} \right)$ for $-1\leq B<A \leq 1$ which consists hypergeometric meromorphic functions of the form $ {L_p^* \left( {a,c} \right)f\left( z \right)}=\frac{1}{z^p} + \sum\limits_{n =... ...frac{{\left( a \right)_{n + 2} }}{{\left( c \right)_{n + 2} }}} a_{n+p} z^{n+p}$ in $U^*= \left\{ {z: 0<\left\vert z \right\vert < 1} \right\}$. We determine sufficient conditions, distortion properties and radii of starlikeness and convexity for functions in the class ${L_p^* \left( {a,c} \right)f\left( z \right)}$.

Received: March 8, 2010

AMS Subject Classification: 30C45, 33C05

Key Words and Phrases: $p$-valent hypergeometric functions, meromorphic functions, starlike functions, convex functions, Hadamard product

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 61
Issue: 3