| Volume 14, Number 5, 2024, Pages - DOI：10.11948/JAAC-2023-0454 |
| Unicity of meromorphic functions concerning derivatives-differences and small functions |
| Ge Wang,Zhiying He,Mingliang Fang |
| Keywords:Entire functions Unicity Difference Small functions |
| Abstract: |
| In this paper, we mainly prove: Let $f$ be a transcendental entire function of finite order with a Borel exceptional entire small function $a$, and let $\eta$ be a nonzero finite complex number such that $\Delta^{n+1}\eta f\not \equiv0$. If $\Delta^{n+1}_\eta f$ and $\Delta^n_\eta f$ share $b$ CM, where $b$ is a small function of $f$, then $f(z)=a(z)+Be^{Az},$ where $A$ and $B$ are two nonzero constants and $a(z)$ is a polynomial with $\deg a\leq n-1$. This improves the results due to Chen and Zhang [Ann. Math. Ser. A (Chinese version) 2021] and Liu and Chen [J. Korean Soc. Math. Educ. Ser. B: Pure Apple. Math. 2023]. Meanwhile, we give negative answer to the problems posed by Chen and Xu [Comput. Methods Funct. Theory, 2022], Banerjee and Maity [Bull. Korean Math. Soc., 2021]. |
PDF Download reader
|
|
|
|