On Sharp Estimate of Third Hankel Determinant for a Subclass of Starlike Functions

Abstract

In our present investigation, a subclass of starlike function Sn−1,L* connected with a domain bounded by an epicycloid with n−1 cusps was considered. The main work is to investigate some coefficient inequalities, and second and third Hankel determinants for functions belonging to this class. In particular, we calculate the sharp bounds of the third Hankel determinant for f∈S4L* with zf′(z)f(z) bounded by a four-leaf shaped domain under the unit disk D.