Hankel determinant of order three for familiar subsets of analytic functions related with sine function

Abstract

In this paper we define and consider some familiar subsets of analytic functions associated with sine functions in the region of unit disk on the complex plane. For these classes our aim is to find the Hankel determinant of order three.

Sharp Bounds of the Coefficient Results for the Family of Bounded Turning Functions Associated with a Petal-Shaped Domain

“…The inequalities (21), (22), (23), and (24) in the above lemma are taken from [43,46], [47][48][49], and [50], respectively.…”

Third Hankel determinant and Zalcman functional for a class of starlike functions with respect to symmetric points related with sine function

“…Babalola [2] was the first person to study the upper bound of H 3,1 (f) for subclass of S. For more details on this topic readers are advised to see the work of several researchers like Zaprawa [35], Raza et al [27], Khan et al [11], Cho et al [5], Lecko et al [13], Srivastava et al [32], and Khan et al [12]. Very recently, Arif et al [1], investigated upper bounds for third hankel determinant for the class of functions S * (Ψ) associated with trigonometric sine function. Stimulated by aforementioned work, we determine the upper bounds of the 3 rd Hankel for the class S * s (Ψ) of symmetric points associated with sine function.…”

Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function

“…They investigated the inverse inclusion relations of this family with the already known subfamilies of analytic functions. Later on for this family, the third Hankel determinants were studied by the authors in [21].…”