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Matematicheskie Zametki, 2005, Volume 78, Issue 4, Pages 537–541
DOI: https://doi.org/10.4213/mzm2612 (Mi mzm2612) 		 
This article is cited in 36 scientific papers (total in 36 papers)

On Brennan's Conjecture for a Special Class of Functions

I. R. Kayumov

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University
Full-text PDF (167 kB) Citations (36)
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DOI: https://doi.org/10.4213/mzm2612
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 $zf'(z)/f(z)$.
Received: 17.12.2004
Revised: 11.04.2005
English version:
Mathematical Notes, 2005, Volume 78, Issue 4, Pages 498–502
DOI: https://doi.org/10.1007/s11006-005-0149-1
Bibliographic databases:
UDC: 517.54
Language: Russian
Citation: I. R. Kayumov, “On Brennan's Conjecture for a Special Class of Functions”, Mat. Zametki, 78:4 (2005), 537–541; Math. Notes, 78:4 (2005), 498–502
Citation in format AMSBIB
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    • This publication is cited in the following 36 articles:
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