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Mathematica Slovaca

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Volume 68, Issue 4

Issues

A uniqueness problem for entire functions related to Brück’s conjecture

Nguyen Van Thin
  • Department of Mathematics, Thai Nguyen University of Education, Luong Ngoc Quyen street, Thai Nguyen city, Vietnam
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/ Ha Tran Phuong
  • Department of Mathematics, Thai Nguyen University of Education, Luong Ngoc Quyen street, Thai Nguyen city, Vietnam
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/ Leuanglith Vilaisavanh
  • Department of Mathematics, Thai Nguyen University of Education, Luong Ngoc Quyen street, Thai Nguyen city, Vietnam
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Published Online: 2018-08-06 | DOI: https://doi.org/10.1515/ms-2017-0148

Abstract

In this paper, we prove a normal criteria for family of meromorphic functions. As an application of that result, we establish a uniqueness theorem for entire function concerning a conjecture of R. Brück. The above uniqueness theorem is an improvement of a problem studied by L. Z. Yang et al. [14]. However, our method differs the method of L. Z. Yang et al. [14]. We mainly use normal family theory and combine it with Nevanlinna theory instead of using only the Nevanlinna theory as in [14].

MSC 2010: Primary 30D45; 30D35

Keywords: Brück’s conjecture; meromorphic functions; Nevanlinna theory; normal family

References

  • [1]

    Brück, R.: On entire functions which share one value CM with their first derivatives, Results Math. 30 (1996), 21–24.CrossrefGoogle Scholar

  • [2]

    Chuang, C. T.: On differential polynomials. In: Analysis of One Complex Variable, World Sci. Publishing, Singapore, 1987, pp. 12–32.Google Scholar

  • [3]

    Clunie, J.—Hayman, W. K.: The spherical derivative of integral and meromorphic functions, Comment. Math. Helv. 40 (1966), 117–148.Google Scholar

  • [4]

    Chen, Z. X.—Shon, K. H.: On conjecture of R. Brück concerning the entire function sharing one value CM with its derivative, Taiwanese J. Math. 8 (2004), 235–244.CrossrefGoogle Scholar

  • [5]

    Dethloff, G.—Tan, T. V.—Thin, N. V.: Normal criteria for families of meromorphic functions, J. Math. Anal. Appl. 411 (2014), 675–683.CrossrefWeb of ScienceGoogle Scholar

  • [6]

    Gundersen, G. G.—Yang, L. Z.: Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl. 223 (1998), 88–95.CrossrefGoogle Scholar

  • [7]

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

  • [8]

    Hinchliffe, J. D.: On a result of Chuang related to Hayman’s Alternative, Comput. Methods Funct. Theory 2 (2002), 293–297.Google Scholar

  • [9]

    Hennekemper, W.: Über die wertverteilung von (fk+1)k, Math. Z. 177 (1981), 375–380.CrossrefGoogle Scholar

  • [10]

    Laine, I.: Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, New York, 1993.Google Scholar

  • [11]

    Schwick, W.: Normality criteria for normal, families of meromorphic function, J. Anal. Math. 52 (1989), 241–289.Google Scholar

  • [12]

    Zalcman, L.: Normal families: New perspective, Bull. Amer. Math. Soc. 35 (1998), 215–230.CrossrefGoogle Scholar

  • [13]

    Zhang, X. B.—Xu, J. F.—Yi, H. X.: Normality criteria of Lahiri’s type and their applications, J. Inequal. Appl. (2011), Article ID 873184.Web of ScienceGoogle Scholar

  • [14]

    Yang, L. Z.—Zhang, J. L.: Non-existence of meromorphic solutions of a Fermat type functional equation, Aequationes Math. 76 (2008), 140–150.CrossrefWeb of ScienceGoogle Scholar

About the article

Received: 2016-09-11

Accepted: 2017-01-17

Published Online: 2018-08-06

Published in Print: 2018-08-28


Communicated by Stanisława Kanas


Citation Information: Mathematica Slovaca, Volume 68, Issue 4, Pages 823–836, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0148.

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