Relation Between Second and Third Coefficients of Taylor’s Expansion of Functions Belonging to A Subclass of Univalent Functions

Abstract

The objective of this paper is to present new class and various subclasses of that class of univalent functions. We discuss approximations on the Taylor–Maclaurin coefficients || and ||, and the Fekete–Szego problem is also considered for the new class and its subclasses of functions introduced. We denote these classes by and will be defined aswill give its various subclasses for different values of the parameters  and will be defined as We obtain a Fekete–Szegö inequality for certain normalized analytic function belonging to these classes and subclasses defined on the open unit disk. As a special case of this result, the Fekete–Szegö inequality for this class of functions defined through extremal function which makes the inequality justified strongly is obtained. We establish the coefficient inequality proved by Fekete and Szegö [5] in 1933 by using the analytic functions of the formf(z) = z +belonging to the newly established class of analytic functions.

2010 Mathematics Subject Classification: 30C45, 30C50.