ENTIRE FUNCTIONS THAT SHARE A SET WITH THEIR DIFFERENCES

Abstract

<abstract> In this paper, we study the uniqueness of entire functions concerning deficient value and exponent of convergence, and have mainly proved the following theorem: Let $S=\{1, \omega , \omega ^2, \cdots , \omega ^{n-1}\}$, where $\omega ^n=1$, $n\ge 1$ is an integer, let $k$ be a positive integer, and let $f$ be a nonconstant entire function such that $\lambda(f)&lt;\rho(f)&lt;\infty$. If $f(z)$ and $\Delta _{\eta }^kf(z)$ share $S$ IM, where $\eta $ is a nonzero complex number, then $f(z)=e^{az+b}$, where $a(\neq0)$ and $b$ are two finite complex numbers. The results obtained in this paper improve some results due to Li ([<xref ref-type="bibr" rid="b15">15</xref>]). </abstract>