On Brennan's Conjecture for a Special Class of Functions.

In this paper, we prove Brennan's conjecture for conformal mappings f of the disk { z : | z| < 1} assuming that the Taylor coefficients of the function log( zf′( z)/ f( z)) at zero are nonnegative. We also obtain inequalities for the integral means over the circle | z| = r of the squared modulus of the function zf′( z)/ f( z). [ABSTRACT FROM AUTHOR]