Fekete-Szegö Problem for a Generalized Subclass of Analytic Functions

• Journal title : Kyungpook mathematical journal
• Volume 53, Issue 1,  2013, pp.13-23
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2013.53.1.13
Title & Authors
Fekete-Szegö Problem for a Generalized Subclass of Analytic Functions
Orhan, Halit; Yagmur, Nihat; Caglar, Murat;

Abstract
In this present work, the authors obtain Fekete-Szeg$\small{\ddot{o}}$ inequality for certain normalized analytic function $\small{f(z)}$ defined on the open unit disk for which $\small{\frac{{\lambda}{\beta}z^3(L(a,c)f(z))^{{\prime}{\prime}{\prime}}+(2{\lambda}{\beta}+{\lambda}-{\beta})z^2(L(a,c)f(z))^{{\prime}{\prime}}+z(L(a,c)f(z))^{{\prime}}}{{\lambda}{\beta}z^2(L(a,c)f(z))^{{\prime}{\prime}}+({\lambda}-{\beta})z(L(a,c)f(z))^{\prime}+(1-{\lambda}+{\beta})(L(a,c)f(z))}\;(0{\leq}{\beta}{\leq}{\lambda}{\leq}1)}$ 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 are obtained.
Keywords
Fekete-Szeg$\small{\ddot{o}}$ problem;Analytic function;Coefficient inequality;
Language
English
Cited by
1.
Coefficient Bounds for Certain Analytic Functions, Bulletin of the Malaysian Mathematical Sciences Society, 2016
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