The Fekete-Szegö Problem for a Generalized Subclass of Analytic Functions

• Journal title : Kyungpook mathematical journal
• Volume 50, Issue 1,  2010, pp.37-47
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2010.50.1.037
Title & Authors
The Fekete-Szegö Problem for a Generalized Subclass of Analytic Functions
Deniz, Erhan; Orhan, Halit;

Abstract
In this present work, the authors obtain Fekete-Szeg$\small{\ddot{o}}$ inequality for certain normalized analytic function f(z) defined on the open unit disk for which $\small{\frac{(1-{\alpha})z(D^m_{{\lambda},{\mu}}f(z))$ $\small{{\alpha}{\geq}0}$) 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 (or convolution) are given. As a special case of this result, Fekete-Szeg$\small{\ddot{o}}$ inequality for a class of functions defined through fractional derivatives is obtained. The motivation of this paper is to generalize the Fekete-Szeg$\small{\ddot{o}}$ inequalities obtained by Srivastava et al., Orhan et al. and Shanmugam et al., by making use of the generalized differential operator $\small{D^m_{{\lambda},{\mu}}}$.
Keywords
Fekete-Szeg$\small{\ddot{o}}$ problem;Analytic functions;Hadamard product;Starlike functions;
Language
English
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