Uniqueness on entire functions and their nth order exact differences with two shared values

Abstract

Let f(z) be an entire function of hyper order strictly less than 1. We prove that if f(z) and its nth exact difference Δcnf(z){\Delta }_{c}^{n}f(z) share 0 CM and 1 IM, then Δcnf(z)≡f(z){\Delta }_{c}^{n}f(z)\equiv f(z). Our result improves the related results of Zhang and Liao [Sci. China A, 2014] and Gao et al. [Anal. Math., 2019] by using a simple method.

Keywords

• entire function
• exact difference
• uniqueness
• shared values
• 30d35
• 39a10