Meromorphic Functions Partially Share Three Values with Their Difference Operators

Abstract

In this paper, the authors firstly give a simple proof and strengthened version of a uniqueness theorem of meromorphic functions which partially share 0, ∞ CM and 1 IM with their difference operators. In addition, they partially solve a conjecture given by Chen-Yi (2013) and generalize some previous theorems by Chen (2018) and Chen-Xu (2022). Furthermore, the authors obtain a uniqueness result of the k-th derivative of meromorphic functions with its shift, which is a generalization of some previous theorems by Chen-Xu (2022), Qi-Li-Yang (2018) and Qi-Yang (2020).

Keywords

Uniqueness / Meromorphic / Difference operator / Shared values / 30D30 / 39A10

References

[1] Chen S J. Some researches on shift operators, difference operators and differential operators of meromorphic functions, 2017, Fuzhou. Fujian Normal University

[2] Chen S J. On uniqueness of meromorphic functions and their difference operators with partially shared values. Comput. Methods Funct. Theory, 2018, 18: 529-536.

[3] Chen S J, Xu A Z. Uniqueness theorem for a meromorphic function and its exact difference. Bull. Korean Math. Soc., 2020, 57: 1307-1317. DOI:

[4] Chen S J, Xu A Z. Uniqueness of derivatives and shifts of meromorphic functions. Comput. Methods Funct. Theory, 2022, 22: 197-205.

[5] Chen Z X, Yi H X. On sharing values of meromorphic functions and their differences. Result Math., 2013, 63: 557-565.

[6] Cui N, Chen Z X. The conjecture on unity of meromorphic functions concerning their differences. J. Difference Equ. Appl., 2016, 22: 1452-1471.

[7] Halburd R G, Korhonen R J, Tohge K. Holomorphic curves with shift-invariant hyperplane preimages. Trans. Amer. Math. Soc., 2014, 366: 4267-4298.

[8] Hayman W K. Meromorphic Functions, 1964, Oxford. Clarendon Press

[9] He C, Lü F. Meromorphic functions partially sharing 1 CM+1 IM concerning periodicities and shifts. Filomat., 2019, 33: 5149-5158.

[10] Lü F, Lü W R. Meromorphic functions sharing three values with their difference operators. Comput. Methods Funct. Theory, 2017, 17: 395-403.

[11] Qi X G, Li N, Yang L Z. Uniquness of meromorphic functions concerning their differences and solutions of difference Painlevé. Comput. Methods Funct. Theory, 2018, 18: 567-582.

[12] Qi X G, Yang L Z. Uniqueness of meromorphic functions concerning their shifts and derivatives. Comput. Methods Funct. Theory, 2020, 20: 159-178.

[13] Yang C C, Yi H X. Uniqueness Theory of Meromorphic Functions, 2003, Dordrecht. Kluwer Academic Publishers.

[14] Zhang J, Liao L W. Entire functions sharing some values with their difference operators. Sci. China Math., 2014, 57: 2143-2152.

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