Hankel determinants for starlike functions associated with a cardioid domain

Abstract

Sharp bounds are given for second and third Hankel determinants, and the Zalcman functional $a_{2}a_{3}-a_{4}$ for starlike functions related to a cardioid domain.

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

“…In 2021, Guney and Korfeci [17] studied the fourth-order Hankel determinant for analytic functions, which are defined by using the modified sigmoid function, Zhang and Tang [18] found the same bound for functions connected with the sine function, Srivastava et al [19] investigated third Hankel for q-starlike functions associated with q-analogue of the exponential function, and Saliu and Noor [20] studied third Hankel for analytic functions which are defined by using the Sȃlȃgean differential and Komatu integral operators. Recently, in 2022, Raza et al [21] studied Hankel determinants for starlike functions connected with symmetric Booth Lemniscate, Khan et al [22] found the bound of third-order Hankel determinants for logarithmic coefficients of starlike functions connected with Sine function, and Riaz et al [23][24][25] studied the Hankel determinants for starlike and convex functions associated with the sigmoid function, lune, and cardioid domain. Now, we intend to find the upper bound of the third-order Hankel determinant for a subclass of starlike univalent functions, denoted by S * qs , which is defined below.…”