Uniqueness of entire functions concerning difference polynomials

Meng, Chao

Mathematica Bohemica, Tome 139 (2014) no. 1, pp. 89-97.

Résumé

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.

Détail

DOI : 10.21136/MB.2014.143638

Classification : 30D35, 39A05
Keywords: entire function; difference polynomial; uniqueness