Research article

On the uniqueness of meromorphic functions that share small functions on annuli

  • Received: 31 December 2019 Accepted: 17 March 2020 Published: 27 March 2020
  • MSC : 30D30, 30D35

  • In this paper, we aim to investigate the uniqueness of meromorphic functions that share small functions on annuli. As a matter of fact, we give several uniqueness theorems about meromorphic functions sharing four or three distinct small functions on the annulus $\mathbb{A} = \{z:\frac{1}{R_{0}} < |z|< R_{0}\},$ where 1 < $R_{0}\leq+\infty.$ To some extent, our theorems extend the previous work by T. B. Cao, H. X. Yi and H. Y. Xu, and also generalize the work by N. Wu and Q. Ge.

    Citation: Da Wei Meng, San Yang Liu, Nan Lu. On the uniqueness of meromorphic functions that share small functions on annuli[J]. AIMS Mathematics, 2020, 5(4): 3223-3230. doi: 10.3934/math.2020207

    Related Papers:

  • In this paper, we aim to investigate the uniqueness of meromorphic functions that share small functions on annuli. As a matter of fact, we give several uniqueness theorems about meromorphic functions sharing four or three distinct small functions on the annulus $\mathbb{A} = \{z:\frac{1}{R_{0}} < |z|< R_{0}\},$ where 1 < $R_{0}\leq+\infty.$ To some extent, our theorems extend the previous work by T. B. Cao, H. X. Yi and H. Y. Xu, and also generalize the work by N. Wu and Q. Ge.


    加载中


    [1] T. B. Cao, H. X. Yi, Uniqueness theorems of meromorphic functions sharing sets IM on annuli, Acta Math. Sinica, 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. doi: 10.1016/j.camwa.2009.07.042
    [3] K. Ishizaki, Meromorphic functions sharing small functions, Arch. Math., 77 (2001), 273-277. doi: 10.1007/PL00000491
    [4] A. Y. Khrystiyanyn, A. A. Kondratyuk, On the Nevanlinna theory for meromorphic functions on annuli. I, Mat. Stud., 23 (2005), 19-30.
    [5] A. Y. Khrystiyanyn, A. A. Kondratyuk, On the Nevanlinna theory for meromorphic functions on annuli. II, Mat. Stud., 24 (2005), 57-68.
    [6] A. A. Kondratyuk, I. Laine, Meromorphic functions in multiply connected domains, Fourier series methods in complex analysis, Univ. Joensuu, 2006.
    [7] R. Korhonen, Nevanlinna theory in an annulus, value distribution theory and related topics, Adv. Complex Anal. Appl., 3 (2004), 167-179.
    [8] Y. H. Li, Entire Functions that Share Four Small Functions IM, Acta Math. Sinica, 3 (1998), 249-260.
    [9] Y. H. Li, J. Y. Qiao, The uniqueness of meromorphic functions concerning small functions, Sci. China Ser. A., 43 (2000), 581-590. doi: 10.1007/BF02908769
    [10] H. F. Liu, Z. Q. Mao, Meromorphic functions in the unit disc that share slowly growing functions in an angular domain, Comput. Math. Appl., 62 (2011), 4539-4546. doi: 10.1016/j.camwa.2011.10.033
    [11] R. Nevanlinna, Eindentig keitssätze in der theorie der meromorphen funktionen, Acta. Math., 48 (1926), 367-391. doi: 10.1007/BF02565342
    [12] N. Wu, Q. Ge, On uniqueness of meromorphic functions sharing five small functions on annuli, Bull. Iranian Math. Soc., 41 (2015), 713-722.
    [13] H. Y. Xu, Z. J. Wu, The shared set and uniqueness of meromorphic functions on annuli, Abstr. Appl. Anal., 2013 (2013), 1-10.
    [14] H. Y. Xu, Z. X. Xuan, The uniqueness of analytic functions on annuli sharing some values, Abstr. Appl. Anal., 2012 (2012), 309-323.
    [15] H. X. Yi, Uniqueness theorems for meromorphic functions concerning small functions, Indian J. pure appl. Math., 32 (2001), 903-914.
    [16] H. X. Yi, C. C. Yang, Uniqueness theory of meromorphic functions, Kluwer Academic Publishers Group, Dordrecht, 2003.
    [17] H. X. Yi, On one problem of uniqueness of meromorphic functions concerning small functions, Proc. Amer. Math. Soc., 130 (2001), 1689-1697. doi: 10.1090/S0002-9939-01-06245-1
    [18] L. Yang, Value Distribution Theory, Science Press, Beijing, 1993.
    [19] J. H. Zheng, On uniqueness of meromorphic functions with shared values in one angular domains, Complex Var. Elliptic Equ., 48 (2003), 777-785.
    [20] J. H. Zheng, On uniqueness of meromorphic functions with shared values in some angular domains, Canad J. Math., 47 (2004), 152-160. doi: 10.4153/CMB-2004-016-1
  • Reader Comments
  • © 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2824) PDF downloads(393) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog