The estimate of the difference of initial successive coefficients of univalent functions

Let A denote the family of all functions that are analytic in the unit disk D := {z : |z| < 1} and satisfy f(0) = 0 = f ′(0) −1. Let S be the set of all functions f ∈A that are univalent in D. In this paper the sharp upper bounds of |a3 −a2| and |a4 −a3| for the functions f(z) = z+∑∞ n=2 anzn being in several subclasses of S are presented. Mathematics subject classification (2010): 30C45.