Some results on entire functions that share one value with their difference operators

Advances in Difference Equations

Fujie Chai¹  Sheng Li²  BaoQin Chen² 

[1] Department of Mathematics, Guangzhou Civil Aviation College;Faculty of Mathematics and Computer Science, Guangdong Ocean University;

关键词: Difference operators;    Entire functions;    Shared values;   

DOI  :  10.1186/s13662-018-1653-4

来源: DOAJ

【 摘 要 】

Abstract In this paper, we give some results on entire functions that share one value with their difference operators. In particular, we prove the following result, which can be regarded as a difference analogue of a result of J.P. Wang and H.X. Yi (J. Math. Anal. Appl. 277:155–163, 2003): Let f(z) $f(z)$ be a non-constant entire function such that ρ2(f)<1 $\rho_{2}(f)<1$, a(≠0) $a (\neq0)$ be a finite constant, and n and m be positive integers satisfying m>n>1 $m>n>1$. If f(z)=a⇌Δcf(z)=a,f(z)=a→Δcmf(z)=Δcnf(z)=a, $$ f(z)=a \rightleftharpoons\Delta_{c}f(z)=a,\qquad f(z)=a \rightarrow \Delta_{c}^{m} f(z)=\Delta_{c}^{n} f(z)=a, $$ then Δcnf(z)≡Δcmf(z) $\Delta_{c}^{n}f(z)\equiv\Delta_{c}^{m}f(z)$. Two related results are proved and an example is provided.

【 授权许可】

Unknown