# Article

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Keywords:
entire function; difference polynomial; uniqueness
Summary:
In this paper, we investigate the uniqueness problem of difference polynomials sharing a small function. With the notions of weakly weighted sharing and relaxed weighted sharing we prove the following: Let $f(z)$ and $g(z)$ be two transcendental entire functions of finite order, and $\alpha (z)$ a small function with respect to both $f(z)$ and $g(z)$. Suppose that $c$ is a non-zero complex constant and $n\geq 7$ (or $n\geq 10$) is an integer. If $f^{n}(z)(f(z)-1)f(z+c)$ and $g^{n}(z)(g(z)-1)g(z+c)$ share “$(\alpha (z),2)$” (or $(\alpha (z),2)^{*}$), then $f(z)\equiv g(z)$. Our results extend and generalize some well known previous results.
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