LOGARITHMIC COEFFICIENTS AND HANKEL DETERMINANT FOR A NEW SUBCLASS OF CLOSE-TO-STAR FUNCTIONS ASSOCIATED WITH THE SINE FUNCTION

Abstract

In this paper, we investigate the logarithmic coefficients for a new subclass of close-to-star functions associated with the sine function. We derive explicit formulas for the first six logarithmic coefficients γ₁ through γ₆ for functions in this class. We obtain upper bounds for the Hankel coefficients, Hankel determinants H_2,1 (f), H_2,2 (f), H_3,1 (f)and H_4,1 (f) associated with the class CST₀ (sin z). In addition, we derive sharp estimates for the Hankel determinant for the logarithmic coefficients H_2,1(F_f /2) and H_2,2 (F_f /2) within the same class.