IJPAM: Volume 79, No. 2 (2012)

DIFFERENTIAL SUBORDINATION AND SUPERORDINATION
OF ANALYTIC FUNCTIONS DEFINED BY A
GENERALIZED DERIVATIVE OPERATOR

N.M. Mustafa$^1$, M. Darus$^2$
$^{1,2}$School of Mathematical Sciences
Faculty of Science and Technology
Universiti Kebangsaan Malaysia
43600, Bangi, Selangor, MALAYSIA


Abstract. Differential subordination and superordination results are obtained for analytic functions in the open unit disk which are associated with the generalized derivative operator $D^{\alpha,\delta}_{p}(\mu,q,\lambda)f(z)$. These results are obtained by investigating appropriate classes of admissible functions. Sandwich-type results are also obtained. Some of the results established in this paper would provide extensions to those given in the earlier works.

Received: June 5, 2012

AMS Subject Classification: 30C45

Key Words and Phrases: analytic function, differential subordination, superordination

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 79
Issue: 2