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

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

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (3): 786-798.doi: 10.1016/S0252-9602(17)30037-1

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

崔宁, 陈宗煊

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

收稿日期:2016-02-17 出版日期:2017-06-25 发布日期:2017-06-25
通讯作者: Zong-Xuan CHEN E-mail:chzx@vip.sina.com
作者简介:Ning CUI,E-mail:cuining588@126.com
基金资助:
This research was supported by the Natural Science Foundation of Guangdong Province in China (2014A030313422,2016A030310106,2016A030313745).

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

Ning CUI, Zong-Xuan CHEN

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

Received:2016-02-17 Online:2017-06-25 Published:2017-06-25
Supported by:
This research was supported by the Natural Science Foundation of Guangdong Province in China (2014A030313422,2016A030310106,2016A030313745).

摘要/Abstract

摘要：

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).

关键词: Entire function, shifts, difference operators, shared values

Abstract:

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

崔宁, 陈宗煊. ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION CM WITH THEIR SHIFTS AND DIFFERENCE OPERATORS[J]. 数学物理学报(英文版), 2017, 37(3): 786-798.

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.

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

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

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