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.

Investigation of the Second-Order Hankel Determinant for Sakaguchi-Type Functions Involving the Symmetric Cardioid-Shaped Domain

“…These two determinants are well-studied in the literature [26][27][28][29] for diverse subfamilies of univalent functions; however, there are very few published papers [30,31], where the determinant's sharp bounds are determined. The interested readers may also appreciate the work of authors [32][33][34][35][36] in which they proved sharp bounds of the third-order Hankel determinant for some novel subfamilies of univalent functions.…”

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

“…For the bounded turning functions R, the sharp upper bound of third Hankel determinant was calculated to be 1 4 in [29]. For some subclasses of convex functions, starlike functions and bounded turning functions, some sharp bounds of third Hankel determinant were also obtained in [30][31][32][33].…”

Sharp Bounds of Hankel Determinant on Logarithmic Coefficients for Functions Starlike with Exponential Function

“…where S * 1 2 indicate the starlike functions family of order 1 2 . For more contributions in this direction, see [29][30][31][32][33][34][35][36][37][38].…”