Certain Coefficient Problems for q-Starlike Functions Associated with q-Analogue of Sine Function

Abstract

This study introduces a subclass Sqs* of starlike functions associated with the q-analogue of the sine function defined in symmetric unit disk. This article comprises the investigation of sharp coefficient bounds, and the upper bound of the third-order Hankel determinant for this class. It also includes the findings of Zalcman and generalized Zalcman conjectures for functions of this class.

On Coefficient Inequalities of Starlike Functions Related to the q-Analog of Cosine Functions Defined by the Fractional q-Differential Operator

“…He and his colleague Bansal explored a very specific set of functions known as q-Mittag-Leffler functions in terms of any of their elements belonging to close-to-convex functions and demonstrated the requirements. This work is available for interested readers in [10]. There are other works that may be cited as references here, but continuing with the same author, we also discovered another article that defined the associated operators in classical, q-, and fractional q-calculus.…”

Second Hankel Determinant and Fekete–Szegö Problem for a New Class of Bi-Univalent Functions Involving Euler Polynomials

“…Contemporary research in geometric function theory places emphasis on the geometric characteristics of specific functions, such as hypergeometric functions, Bessel functions, and other associated functions. In relation to certain geometric properties of these functions, we make reference to [12][13][14][15][16][17][18] and any other pertinent sources. This paper introduces a novel category of bi-univalent functions and employs a specific function known as the Euler polynomial.…”

Editorial Conclusion for the Special Issue “Applications of Symmetric Functions Theory to Certain Fields”

“…Taj et al [1] introduced a subclass of starlike functions associated with the q-analogue of the sine function defined in symmetric unit disk. They investigated the sharp coefficient bounds and upper bound of the third-order Hankel determinant for this class.…”