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

Abstract

In this article we define a class of starlike functions with respect to symmetric points in the domain of sine function. Also, we investigate coefficients bounds and upper bounds for the third order Hankel determinant for this defined class. We also evaluate the Zalcman functional |a 2 3 − a 5 |. Specializing the parameters, we improve Zalcman functional for the class of starlike functions.

Fekete-Szego and Zalcman Functional Estimates for Subclasses of Alpha-Convex Functions Related to Trigonometric Functions

“…It is noteworthy that for n = 2 the above inequality is a well-known consequence of the Area Theorem and could be found in [1,Theorem 1.5]. In the recent years the Zalcman functional has been given a special interest by many researchers (see, for example, [17][18][19]).…”

Fekete–Szegő and Zalcman Functional Estimates for Subclasses of Alpha-Convex Functions Related to Trigonometric Functions

“…It is noteworthy that, for n = 2, the above inequality is a well-known consequence of the well-known Area Theorem and can be found in Theorem 1.5 of [1]. In recent years, the Zalcman functional has received special interest from many researchers (see, for example, [18][19][20]).…”

Coefficient Inequalities for Certain Subclass of Starlike Function with respect to Symmetric points related to q-exponential Function

“…Other researchers like Vamshee Krishna et al [28], Patil and Khairnar [29], Prajapat et al [30], Yalcin and Altinkaya [31], Cho et al [32], Lecko et al [33]. Kowalczyk et al [34], Mohd Narzan et al [35], Several other researchers like Mendiratta et al [36], Haiyan Zhang et al [37], khan et al [38], and Senguttuvan et al [39] defined A thorough sub-class of analytic functions with respect to the symmetrical point that has been developed. The current study is expanded by using quantum calculus and tends to investigate the upper bounds of the 3rd Hankel Determinant, for the classes of a star-like function with respect to symmetrical points subordinate to exponential functions.…”