Some application of Grunsky coefficients in the theory of univalent functions

Let function f be normalized, analytic and univalent in the unit disk 𝔻 = { z : | z | < 1} and f ( z ) = z + ∑ n = 2 ∞ a n z n f( z ) = z + ∑n = 2^∞ {{a_n}{z^n}} . Using a method based on Grusky coefficients we study several problems over that class of univalent functions: upper bounds of the special case of the generalized Zalcman conjecture | a 2 a 3 − a 4 |, of the third logarithmic coefficient, and of the second Hankel determinant for the logarithmic coefficients.