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

In the present paper, we give a new simple proof on the sharp bounds of coefficient functionals related to the Caratheodory 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-P associated with a cardioid domain. For functions in this class, we calculate the bounds of the Fekete-Szego-type inequality and the second- and third-order Hankel determinants. All the results are proved to be sharp.

Automated summary

In this paper, a new simple proof is provided for the sharp bounds of coefficient functionals related to Caratheodory functions, and a correction on the extremal functions is made. The result is then applied to investigate the initial coefficient bounds of a subclass of bounded turning functions R-P associated with a cardioid domain. The bounds of the Fekete-Szego-type inequality and the second- and third-order Hankel determinants are calculated for functions in this class, and all the results are proven to be sharp.