Integral estimates for derivatives of univalent functions

Abstract

© 2014, Pleiades Publishing, Ltd. Brennan’s conjecture for a conformal mapping f of the unit disk is proved under a certain condition on the Taylor coefficients of ln f′. Brennan’s conjecture is also proved in the case where 1/f′ expands into a series of simple fractions absolutely converging to zero. An estimate for the approximation of 1/f′ by simple fractions is obtained.