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

Abstract

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)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.

Keywords

• Difference operators
• Entire functions
• Shared values