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AIMS Mathematics

2020, Volume 5, Issue 6: 7438-7457. doi: 10.3934/math.2020476
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Research article

Uniqueness of meromorphic functions sharing small functions in the k-punctured complex plane

  • 1.
    School of Science, Jiangxi University of Science and Technology, Ganzhou, Jiangxi, 341000, P. R. China
  • 2.
    Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen, Jiangxi, 333403, P. R. China
  • Received: 16 June 2020 Accepted: 14 September 2020 Published: 21 September 2020

  • MSC : 30D30, 30D35

  • The main purpose of this article is concerned with the uniqueness of meromorphic functions in the $k$-punctured complex plane $\Omega$ sharing five small functions with finite weights. We proved that for any two admissible meromorphic functions $f$ and $g$ in $\Omega$, if $\widetilde{E}_\Omega(\alpha_j, l;f) = \widetilde{E}_\Omega(\alpha_j, l; g)$ and an integer $l\geq 22$, then $f\equiv g$, where $\alpha_j~(j = 1, 2, \ldots, 5)$ are five distinct small functions with respect to $f$ and $g$. Our results are extension and improvement of previous theorems given by Ge and Wu, Cao and Yi.

    Citation: Xian Min Gui, Hong Yan Xu, Hua Wang. Uniqueness of meromorphic functions sharing small functions in the k-punctured complex plane[J]. AIMS Mathematics, 2020, 5(6): 7438-7457. doi: 10.3934/math.2020476

    Related Papers:

  • The main purpose of this article is concerned with the uniqueness of meromorphic functions in the $k$-punctured complex plane $\Omega$ sharing five small functions with finite weights. We proved that for any two admissible meromorphic functions $f$ and $g$ in $\Omega$, if $\widetilde{E}_\Omega(\alpha_j, l;f) = \widetilde{E}_\Omega(\alpha_j, l; g)$ and an integer $l\geq 22$, then $f\equiv g$, where $\alpha_j~(j = 1, 2, \ldots, 5)$ are five distinct small functions with respect to $f$ and $g$. Our results are extension and improvement of previous theorems given by Ge and Wu, Cao and Yi.


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    [1] T. B. Cao, H. X. Yi, Uniqueness theorems of meromorphic functions sharing sets IM on annuli, Acta Math. Sin., 54 (2011), 623-632.
    [2] T. B. Cao, H. X. Yi, H. Y. Xu, On the multiple values and uniqueness of meromorphic functions on annuli, Comput. Math. Appl., 58 (2009), 1457-1465.
    [3] M. Fang, Uniqueness of admissible meromorphic functions in the unit disc, Sci. China Ser. A, 42 (1999), 367-381.
    [4] M. O. Hanyak, A. A. Kondratyuk, Meromorphic functions in m-punctured complex planes, Mat. Stud., 27 (2007), 53-69.
    [5] W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
    [6] A. Y. Khrystiyanyn, A. A. Kondratyuk, On the Nevanlinna theory for meromorphic functions on annuli. I, Mat. Stud., 23 (2005), 19-30.
    [7] A. Y. Khrystiyanyn, A. A. Kondratyuk, On the Nevanlinna theory for meromorphic functions on annuli. Ⅱ, Mat. Stud., 24 (2005), 57-68.
    [8] A. A. Kondratyuk, I. Laine, Meromorphic functions in multiply connected domains, In: Fourier Series Methods in Complex Analysis (Mekrijärvi, 2005), Univ. Joensuu Dept. Math. Rep. ser., 10 (2006), 9-111.
    [9] R. Korhonen, Nevanlinna theory in an annulus, value distribution theory and related topics, Advances in Complex Analysis and Its Applications, 3 (2004), 167-179.
    [10] B. Q. Li, Uniqueness of entire functions sharing four small functions, Am. J. Math., 119 (1997), 841-858.
    [11] Y. Li, J. Qiao, The uniqueness of meromorphic functions concerning small functions, Sci. China Ser. A, 43 (2000), 581-590.
    [12] H. Liu, Z. Mao, On uniqueness of meromorphic functions sharing five small functions in some angular domains, Taiwan. J. Math., 17 (2013), 1779-1790.
    [13] D. W. Meng, S. Y. Liu, N. Lu, Uniqueness of meromorphic functions sharing four small functions on annuli, Math. Slovaca, 69 (2019), 815-824.
    [14] N. Wu, Q. Ge, On uniqueness of meromorphic functions sharing five small functions on annuli, Bull. Iran. Math. Soc., 41 (2015), 713-722.
    [15] H. Y. Xu, Y. M. Li, S. Liu, The partially shared values and small functions for meromorphic functions in a k-punctured complex plane, J. Inequal. Appl., 2019 (2019), 1-15.
    [16] H. Y. Xu, S. Y. Liu, The uniqueness of meromorphic functions in k-punctured complex plane, Open Math., 15 (2017), 724-733.
    [17] H. Y. Xu, S. Y. Liu, Q. P. Li, Entire solutions for several systems of nonlinear difference and partial differential-difference equations of Fermat-type, J. Math. Anal. Appl., 483 (2020), 1-20.
    [18] H. Y. Xu, H. Wang, Notes on the Existence of Entire Solutions for Several Partial DifferentialDifference Equations, Bull. Iran. Math. Soc., 2020.
    [19] W. H. Yao, Meromorphic functions sharing four small functions on 2CM+2IM, Arch. Math., 81 (2003), 666-677.
    [20] L. Yang, Value distribution theory, Springer-Verlag Berlin Heidelberg, 1993.
    [21] C. C. Yang, H. X. Yi, Uniqueness theory of meromorphic functions, Kluwer Academic Publishers and Science Press, 2003.
    [22] H. X. Yi, On one problem of uniqueness of meromorphic functions concerning small functions, P. Am. Math. Soc., 130 (2002), 1689-1697.
    [23] H. X. Yi, Y. H. Li, Meromorphic functions that share four small functions, Chinese Ann. Math. Ser. A, 22 (2001), 271-278.
    [24] J. H. Zheng, On uniqueness of meromorphic functions with shared values in some angular domains, Can. Math. Bull., 47 (2004), 152-160.
    [25] J. H. Zheng, On uniqueness of meromorphic functions with shared values in one angular domains, Complex Variables, Theory and Application: An International Journal, 48 (2003), 777-785.
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  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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