Faber Polynomial Coefficient Estimates for Subclass of Analytic Bi-Bazilevic Functions Defined by Differential Operator

Abstract

In this work, an explicit formula for a class of Bi-Bazilevic univalent functions involving differential operator is given, as well as the determination of upper bounds for the general Taylor-Maclaurin coefficient of a functions belong to this class, are established Faber polynomials are used as a coordinated system to study the geometry of the manifold of coefficients for these functions. Also determining bounds for the first two coefficients of such functions.
 In certain cases, our initial estimates improve some of the coefficient bounds and link them to earlier thoughtful results that are published earlier.