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Sbornik: Mathematics, 2017, Volume 208, Issue 3, Pages 360–376
DOI: https://doi.org/10.1070/SM8802 (Mi sm8802) 		 
This article is cited in 23 scientific papers (total in 23 papers)

Holomorphic mappings of the unit disc into itself with two fixed points

V. V. Goryainov

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
English version PDF (473 kB) Citations (23) Russian version article
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DOI: https://doi.org/10.1070/SM8802
Abstract: The paper is concerned with holomorphic mappings of the unit disc into itself with two fixed points. Two cases are considered: when one fixed point lies inside the disc and the other lies on the boundary and when both fixed points lie on the boundary. The effect that angular derivatives at boundary fixed points have on the properties of functions inside the unit disc is studied. Conditions on the angular derivatives to guarantee the existence of domains of univalence inside the unit disc are given. The effect of the angular derivatives on the values of the Taylor coefficients of functions is also examined.
Bibliography: 19 titles.
Keywords: holomorphic mapping, fixed point, domain of univalence, angular derivative, coefficient region.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00674-a
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 16-01-00674_a).
Received: 22.08.2016 and 17.10.2016
Bibliographic databases:
Document Type: Article
UDC: 517.54
MSC: Primary 30C55; Secondary 30C50, 30J99, 30C75
Language: English
Original paper language: Russian
Citation: V. V. Goryainov, “Holomorphic mappings of the unit disc into itself with two fixed points”, Sb. Math., 208:3 (2017), 360–376
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM8802
  • https://www.mathnet.ru/eng/sm/v208/i3/p54
    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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