On Brennan's Conjecture for a Special Class of Functions |
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| Authors: | I. P. Kayumov |
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| Affiliation: | (1) N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University, Kazan, Russia |
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| Abstract: | 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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| Keywords: | Brennan's conjecture univalent analytic function Koebe function conformal mapping fractal boundary |
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