Sharp Coefficient Bounds for a Subclass of Bounded Turning Functions with a Cardioid Domain

Abstract

In the present paper, we give a new simple proof on the sharp bounds of coefficient functionals related to the Carathéodory functions and make a correction on the extremal functions. The result is further used to investigate some initial coefficient bounds on a subclass of bounded turning functions R℘ associated with a cardioid domain. For functions in this class, we calculate the bounds of the Fekete–Szegö-type inequality and the second- and third-order Hankel determinants. All the results are proved to be sharp.

Keywords

• univalent function
• cardioid domain
• coefficient bounds
• Hankel determinant