Third Hankel Determinant for Subclasses of Analytic and <i>m</i>-Fold Symmetric Functions Involving Cardioid Domain and Sine Function

Abstract

In this research, we define a few subclasses of analytic functions which are connected to sine functions and the cardioid domain in the unit disk. We investigate initial coefficient bounds, the Fekete–Szego problem and second and third Hankel determinants for the functions f belonging to these newly defined classes. We also define the class of m-fold symmetric functions related with the sine function and then investigate the bounds of the third Hankel determinant for twofold symmetric and threefold symmetric functions.

Keywords

• analytic functions
• cardioid domain starlike functions
• Hankel determinant
• subordination
• m-fold symmetric functions