The coefficient estimation for harmonic automorphisms of the disk (Q1589066)

A complex-valued harmonic function \(f\) in the unit disk can be represented in the form \(f= h+\overline g\), where \(h\) and \(g\) are analytic. In the paper the exact bound of \(\text{Re}\{c_{n+1}- c_n\}\) is obained for preserving orientation harmonic self-mappings of the unit disk, where \(c_n\), \(n= 1,2,\dots\), are coefficients of the analytic part of \(f\). The method suggested by P. Duren and G. Schober is used.