IJPAM: Volume 69, No. 4 (2011)

HANKEL DETERMINANT FOR A CLASS OF ANALYTIC
FUNCTIONS INVOLVING A GENERALIZED LINEAR
DIFFERENTIAL OPERATOR

Afaf Abubaker$^1$, Maslina Darus$^2$
School of Mathematical Sciences
Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Bangi, Selangor D. Ehsan, 43600, MALAYSIA
$^1$e-mail: m.afaf48@yahoo.com
$^2$e-mail: maslina@ukm.my


Abstract. By making use of the linear differential operator $D_{\alpha ,\mu }^{\sigma ,\rho }$ defined recently by the authors, a class of analytic functions is introduced. The sharp upper bound for the nonlinear functional $\left\vert a_{2} a_{4}- a_{3}^{2}\right\vert$ is obtained.

Received: February 20, 2011

AMS Subject Classification: 30C45

Key Words and Phrases: Fekete-Szegö functional, Hankel determinant, positive real functions, linear differential operator

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 4