Gen. Math. Notes, Vol. 21, No. 1, March 2014, pp. xx-xx
ISSN 2219-7184; Copyright © ICSRS Publication, 2014
www.i-csrs.org
Available free online at http://www.geman.in
Fekete-Szegö Inequality for a New Class and
Its Certain Subclasses of Analytic Functions
Gurmeet Singh
Khalsa College, Patiala
E-mail: meetgur111@gmail.com
(Received: / Accepted:)
Abstract
We introduce some classes of analytic functions, its subclasses and obtain
sharp upper bounds of the functional |
3
− μ
2
2
| for the analytic function
= +
∞
=2
, <1 belonging to these classes and subclasses.
Keywords: Univalent functions, Starlike functions, Close to convex functions
and bounded functions.
1 Introduction
Let denote the class of functions of the form
= +
∞
=2
(1.1)
which are analytic in the unit disc ={:|| < 1|}. Let be the class of
functions of the form (1.1), which are analytic univalent in .
In 1916, Bieber Bach ( [7], [8] ) proved that
2
2 for the functions (). In
1923, Löwner [5] proved that
3
3 for the functions ().