A Comprehensive subclass of analytic and bi-univalent functions associated with subordination

Abstract

In the present paper, we define a new general subclass of bi-univalent functions involving a differential operator in the open unit disk U. For this purpose, we use the Faber polynomial expansions. Several connections to some of the earlier known results are also pointed out.The Koebe one-quarter theorem (for details, (see [10]), we know that the image of U under every function f ∈ A contains a disk of radius 1 4 . According to this, every function f ∈ A has an inverse map f −1 that satisfies the following conditions:and 2010 Mathematics Subject Classification. 30C45.

Hankel Determinant for Starlike and Convex Functions of Order Α/2

“…We employ techniques similar to these used earlier by Amourah et al ( [15], [16], [17], [18], [20]) and Al-Hawary et al [19].…”