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

This article is cited in 12 scientific papers (total in 12 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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\paper On Brennan's Conjecture for a Special Class of Functions
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\issue 4
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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. Alimohammadi D., Adegani E.A., Bulboaca T., Cho N.E., “Logarithmic Coefficients For Classes Related to Convex Functions”, Bull. Malays. Math. Sci. Soc.  crossref  isi
    2. 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
    3. 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
    4. 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
    5. 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
    6. 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
    7. 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
    8. Adegani E.A., Cho N.E., Jafari M., “Logarithmic Coefficients For Univalent Functions Defined By Subordination”, Mathematics, 7:5 (2019), 408  crossref  isi
    9. Ponnusamy S., Sharma N.L., Wirths K.-J., “Logarithmic Coefficients Problems in Families Related to Starlike and Convex Functions”, J. Aust. Math. Soc., 109:2 (2020), 230–249  crossref  mathscinet  isi
    10. Ebadian A., Mohammed N.H., Adegani E.A., Bulboaca T., “New Results For Some Generalizations of Starlike and Convex Functions”, J. Funct. space, 2020 (2020), 7428648  crossref  mathscinet  isi
    11. Alimohammadi D., Cho N.E., Adegani E.A., Motamednezhad A., “Argument and Coefficient Estimates For Certain Analytic Functions”, Mathematics, 8:1 (2020), 88  crossref  isi
    12. Ebadian A., Bulboaca T., Cho N.E., Adegani E.A., “Coefficient Bounds and Differential Subordinations For Analytic Functions Associated With Starlike Functions”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 114:3 (2020), 128  crossref  mathscinet  isi
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