Hankel and Toeplitz determinant for a subclass of multivalent $ q $-starlike functions of order $ \alpha $

Fourth Toeplitz Determinants for Starlike Functions Defined by Using the Sine Function

“…On the other hand, Thomas et al [3] and Ali et al [17] studied Toeplitz matrices whose elements are the coefficients of starlike, close-to-convex, and univalent functions. Besides, Tang et al [18] studied third-order Hankel and Toeplitz determinant for a subclass of multivalent q-starlike functions of order α; Zhang et al [19] considered third-order Hankel and Toeplitz determinants of starlike functions, which are defined by using the sine function; Ramachandran et al [20] derived an estimation for the Hankel and Topelitz determinant with domains bounded by conical sections involving Ruscheweygh derivative; Srivastava et al [21] found the Hankel determinant and the Toeplitz matrices for this newlydefined class of analytic q-starlike functions. Based on the work of Shi et al [14], Zhang and Tang [16], Thomas and Halim [3], and Ali et al [17], in the present paper, we aim to investigate the fourth-order Toeplitz determinant T 4 ð2Þ for this function class S * s associated with sine function and obtain the upper bounds for the determinants T 4 ð2Þ.…”

Multivalent Functions and Differential Operator Extended by the Quantum Calculus

“…This calculus proved its efficiency and accuracy to generalize the families of differential and integral operators in a complex domain. In addition, special functions (see [7,8]) have associated with this calculus, especially the queen of special functions: Mittag-Leffler function (see [9][10][11][12]). The quantum calculus (q-calculus) has tremendous applications in different fields, for example, integral inequalities [13], summability [14], approximation and polynomials [15], and sequence spaces [16].…”

Symmetric Toeplitz Matrices for a New Family of Prestarlike Functions

“…Very recently, several authors established estimates of the Toeplitz determinant T q (n) for functions belonging to various families of univalent functions (see, for example, [7][8][9][10][11][12][13]).…”