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Mat. Zametki, 2005, Volume 78, Issue 4, Pages 537–541 (Mi mz2612)  

This article is cited in 7 scientific papers (total in 7 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

Abstract: In this paper, we prove Brennan's conjecture for conformal mappings $f$ of the disk $ż:|z|<1\}$ 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 $zf'(z)/f(z)$.

DOI: https://doi.org/10.4213/mzm2612

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English version:
Mathematical Notes, 2005, 78:4, 498–502

Bibliographic databases:

UDC: 517.54
Received: 17.12.2004
Revised: 11.04.2005

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. R. Kayumov, “Spektr integralnykh srednikh i zakon povtornogo logarifma dlya konformnykh otobrazhenii”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 148, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2006, 85–96  mathnet  zmath
    2. Jian-Lin Li, “On the Logarithmic Coefficients and Integral Means of Univalent Functions”, Math. Notes, 85:1 (2009), 120–122  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. F. D. Kayumov, “Integralnye otsenki dlya proizvodnykh odnolistnykh funktsii”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 155, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2013, 83–90  mathnet
    4. F. D. Kayumov, “Integralnye otsenki dlya beskonechnykh proizvedenii tipa Rissa”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 155, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2013, 55–60  mathnet
    5. I. R. Kayumov, “Obzor po otsenkam spektra integralnykh srednikh konformnykh otobrazhenii”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2015, 104–115  mathnet  elib
    6. Kayumov I.R., Ponnusamy S., Le Anh Xuan, “On the Analytic Part of Univalent Harmonic Mappings”, Complex Anal. Oper. Theory, 12:5 (2018), 1291–1301  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Adegani E.A., Cho N.E., Jafari M., “Logarithmic Coefficients For Univalent Functions Defined By Subordination”, Mathematics, 7:5 (2019), 408  crossref  isi
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