Bounds on the Third Order Hankel Determinant for Certain Subclasses of Analytic Functions

Abstract

Let A be the class of analytic functions f(z) in the unit disc ∆ = {z ∈ C : |z| < 1g with the Taylor series expansion about the origin given by f(z) = z+ ∑n=2∞ anzn, z ∈∆ : The focus of this paper is on deriving upper bounds for the third order Hankel determinant H3(1) for two new subclasses of A.

Keywords

• analytic functions
• hankel determinant
• functions with positive real part
• primary 30c45
• secondary 30c50