Coefficient Problems in a Class of Functions with Bounded Turning Associated with Sine Function

Abstract

The Hankel determinant for a function having power series was first defined by Pommerenke. The growth of Hankel determinant has been evaluated for different subcollections of univalent functions. Many subclasses with bounded turning are several interesting geometric properties. In this paper, some classes of functions with bounded turning which connect to the sine function are studied in the region of the unit disc in order. Our purpose is to obtain some upper bounds for the third and fourth Hankel determinants related to such classes.

Coefficient functionals for a class of bounded turning functions connected to three leaf function

“…Motivated by all works mentioned above and [15], in this article we introduce and investigate the class R 3L which is defined as follows:…”

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

“…is known as third order Hankel determinant. 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.…”

Third Hankel Determinant For A Class Of Starlike Functions Associated With Exponential Function

“…Some interesting domains on which the Hankel determinant for starlike class was estimated by including k-Fibonacci numbers, Shafiq et al [21] estimated the bounds of the third Hankel determinant for the same. To read more on this work, one can refer [22,6,7,3,11].…”