Two applications of Grunsky coefficients in the theory of univalent functions

Abstract

Let S denote the class of functions f which are analytic and univalent in the unit disk D = {z : |z| < 1} and normalized with f (z) = z + ∞ n=2 anz n . Using a method based on Grusky coefficients we study two problems over the class S: estimate of the fourth logarithmic coefficient and upper bound of the coefficient difference |a 5 | − |a 4 |.