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Mathematica Slovaca

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Volume 68, Issue 4


On characteristic of bounded analytic functions involving hyperbolic derivative

Nan Wu
  • Department of Mathematics School of Science China University of Mining and Technology (Beijing) Beijing-100083 P. R. China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2018-08-06 | DOI: https://doi.org/10.1515/ms-2017-0147


In this article, we give the Nevanlinna type hyperbolic characteristics in simply connected domains and angular domains and the Tsuji type hyperbolic characteristics for bounded analytic functions for the first time. The first fundamental theorems are also established concerning hyperbolic derivative for bounded analytic functions in simply connected domains and angular domains. This is a continuous work of Makhmutov [3].

MSC 2010: Primary 30D10; Secondary 30D20; 30B10; 34M05

Keywords: hyperbolic derivative; Nevanlinna characteristic; Tsuji characteristic


  • [1]

    Goldberg, A. A.—Ostrovskii, I. V.: The distribution of values of meromorphic functions (in Russian), Izdat. Nauk. Moscow, 1970. English translation by Mikhail Ostrovskii, Transl. Math. Monogr. 236, American Mathematical Society, Providence, RI, 2008.Google Scholar

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    Hayman W. K.: Meromorphic Functions, Oxford, 1964.Google Scholar

  • [3]

    Makhmutov, S.: Value distribution of bounded analytic functions, New Zealand J. Math. 39 (2009), 19–24.Google Scholar

  • [4]

    Tsuji, M.: Potential Theory in Modern Function Theory, Maruzen Co., LTD Tokyo, 1959.Google Scholar

  • [5]

    Zheng, J. H.: Value Distribution of Meromorphic Functions, Tsinghua University Press and Springer-Verlag, Beijing and Berlin, 2010.Google Scholar

About the article

Received: 2016-03-20

Accepted: 2017-04-11

Published Online: 2018-08-06

Published in Print: 2018-08-28

Communicated by Stanisława Kanas

Citation Information: Mathematica Slovaca, Volume 68, Issue 4, Pages 811–822, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0147.

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