Geodesic
On Brennan's Conjecture for a Special Class of Functions
Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 537-541.

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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 $zf'(z)/f(z)$. 
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I. R. Kayumov. On Brennan's Conjecture for a Special Class of Functions. Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 537-541. http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a4/

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