IJPAM: Volume 71, No. 4 (2011)

ON FEKETE-SZEGÖ PROBLEMS FOR
CERTAIN SUBCLASS OF ANALYTIC FUNCTIONS

E.A. Eljamal$^1$, M. Darus$^2$
$^1,2$School of Mathematical Sciences
Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Bangi, 43600, Selangor, D. Ehsan, MALAYSIA


Abstract. In this present investigation, the authors obtain Fekete-Szegö inequality for certain normalized analytic function $f(z)$ defined on the open unit disk for which $\frac{z(D^{n,m}_{\lambda_1,\lambda_2}f(z))'}{D^{n,m}_{\lambda_1,\lambda_2}f(z)}$, $(n,m\in N_0 ,\lambda_2\geq\lambda_1\geq0)$ lies in a region starlike with respect to $1$ and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by Hadamard product (convolutionn)are given. As a special case of the result, Fekete-Szegö inequality for a class of functions defined through fractional derivatives is obtained. the motivation of this paper is to give a generalization of the Fekete-Szegö inequalities obtained by Srivasatava and Mishra by making use of $D^{n,m}_{\lambda_1,\lambda_2}f(z)$ the generalized Ruscheweyh derivatives operator introduced by authors [#!Eljamal_and_Darus!#].

Received: April 7, 2011

AMS Subject Classification: 30C45

Key Words and Phrases: analytic function, starlike functions, subordination, Fekete-Szegö inequality, derivative 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: 71
Issue: 4