Some unity results on entire functions and their difference operators related to 4 CM theorem

Journal of inequalities and applications

article

BaoQin Chen¹  Sheng Li¹ 

[1] Faculty of Mathematics and Computer Science, Guangdong Ocean University;Southern Marine Science and Engineering Guangdong Laboratory (Zhanjiang)

关键词: Entire functions;    Differences;    Shared values;    Nevanlinna theory;   

DOI  :  10.1186/s13660-020-02487-6

学科分类：电力

来源: SpringerOpen

【 摘 要 】

This paper is to consider the unity results on entire functions sharing two values with their difference operators and to prove some results related to 4 CM theorem. The main result reads as follows: Let $f(z)$ be a nonconstant entire function of finite order, and let $a_{1}$ , $a_{2}$ be two distinct finite complex constants. If $f(z)$ and $\Delta _{\eta }^{n}f(z)$ share $a_{1}$ and $a_{2}$ “CM”, then $f(z)\equiv \Delta _{\eta }^{n} f(z)$ , and hence $f(z)$ and $\Delta _{\eta }^{n}f(z)$ share $a_{1}$ and $a_{2}$ CM.

【 授权许可】

CC BY