Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions

Abstract

The main purpose of this article is to find the upper bound of the third Hankel determinant for a family of q-starlike functions which are associated with the Ruscheweyh-type q-derivative operator. The work is motivated by several special cases and consequences of our main results, which are pointed out herein.

An Investigation of the Third Hankel Determinant Problem for Certain Subfamilies of Univalent Functions Involving the Exponential Function

“…for the recognizable sets K and S * (1/2) respectively, where the symbol S * (1/2) indicates to the family of starlike functions of order 1/2. Also we would like to cite the work done by Mahmood et al [44] in which they studied third Hankel determinant for a subset of starlike functions in q-analogue. Additionally Zhang et al [45] studied this determinant for the set S * e and obtained the bound…”

Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli

“…The Hankel determinant plays a vital role in the theory of singularities [17] and is useful in the study of power series with integer coefficients (see [18][19][20]). Noteworthy, several authors obtained the sharp upper bounds on H 2 (2) (see, for example, [5,[21][22][23][24][25][26][27][28][29]) for various classes of functions. It is a well-known fact for the Fekete-Szegö functional that:…”

A Study of Third Hankel Determinant Problem for Certain Subfamilies of Analytic Functions Involving Cardioid Domain

“…for the recognizable families K and S * (1/2), respectively, where the symbol S * (1/2) stands for the family of starlike functions of order 1/2. Furthermore, we would like to cite the work done by Mahmood et al [44] in which they studied the third Hankel determinant for a subfamily of starlike functions in the q-analogue. Additionally, Zhang et al [45] studied this determinant for the family S * e and obtained the bound |H 3,1 ( f )| ≤ 0.565.…”