Starlikeness Associated with the Van Der Pol Numbers

In this paper, we define a subclass of starlike functions associated with the Van der Pol numbers. For this class, we derive structural formula, radius of starlikeness of order a, strong starlikeness, and some inclusion results. We also study radii problems for various classes of analytic functions. Furthermore, we investigate some coefficient-related problems which include the sharp initial coefficient bounds and sharp bounds on Hankel determinants of order two and three.

Automated summary

In this paper, a subclass of starlike functions related to the Van der Pol numbers is defined. Structural formula, radius of starlikeness of order a, strong starlikeness, and some inclusion results are derived for this class. Radii problems for various classes of analytic functions are also studied. Furthermore, coefficient-related problems including sharp initial coefficient bounds and sharp bounds on Hankel determinants of order two and three are investigated.