Some Coefficient Estimates for Subclass of Starlike Functions Associated with the Sine Function Defined by Subordination (Thamar University Journal of Natural & Applied Sciences, 2025)
In this paper, we investigate the logarithmic coefficients for a subclass of starlike functions with respect to symmetric conjugate points associated with the sine function. Although this class has been previously studied in the context of coefficient bounds and geometric properties, the logarithmic coefficients, especially higher-order ones, have not been extensively addressed in the literature. We derive explicit formulas for the first six logarithmic coefficients γ1 through γ6 for functions in this class. We establish precise bounds for the Hankel coefficients, Hankel determinants H2,1(f), H2,2(f), H3,1(f), and H4,1(f) associated with the class S*sc(sin z). In addition, we derive sharp estimates for the Hankel determinant for the Logarithmic coefficients H2,1(Ff /2) and H2,2(Ff /2) within the same class.