ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION CM WITH THEIR SHIFTS AND DIFFERENCE OPERATORS

Ning CUI; Zong-Xuan CHEN

doi:10.1016/S0252-9602(17)30037-1

Acta mathematica scientia, Series B >

2017 , Vol. 37 >Issue 3: 786 - 798

DOI: https://doi.org/10.1016/S0252-9602(17)30037-1

Articles

ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION CM WITH THEIR SHIFTS AND DIFFERENCE OPERATORS

Ning CUI ,
Zong-Xuan CHEN

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School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Received date: 2016-02-17

Online published: 2017-06-25

Supported by

This research was supported by the Natural Science Foundation of Guangdong Province in China (2014A030313422,2016A030310106,2016A030313745).

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Abstract

In this article, we mainly devote to proving uniqueness results for entire functions sharing one small function CM with their shift and difference operator simultaneously. Let f(z) be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f(z), f(z+c), and Δ_cⁿf(z) share 0 CM, then f(z + c) ≡ Af(z), where A(≠0) is a complex constant. Moreover, let a(z), b(z)(? 0) ∈ S(f) be periodic entire functions with period c and if f(z) -a(z), f(z + c) -a(z), Δ_cⁿf(z) -b(z) share 0 CM, then f(z + c) ≡ f(z).

Key words： Entire function; shifts; difference operators; shared values

Cite this article

Ning CUI , Zong-Xuan CHEN . ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION CM WITH THEIR SHIFTS AND DIFFERENCE OPERATORS[J]. Acta mathematica scientia, Series B, 2017 , 37(3) : 786 -798 . DOI: 10.1016/S0252-9602(17)30037-1

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