ENTIRE FUNCTIONS THAT SHARE A SET WITH THEIR DIFFERENCES

Jinyu Fan; Jianbin Xiao; Mingliang Fang

doi:10.11948/20210260

2022 Volume 12 Issue 2

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Jinyu Fan, Jianbin Xiao, Mingliang Fang. ENTIRE FUNCTIONS THAT SHARE A SET WITH THEIR DIFFERENCES[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 662-675. doi: 10.11948/20210260

Citation:

Jinyu Fan, Jianbin Xiao, Mingliang Fang. ENTIRE FUNCTIONS THAT SHARE A SET WITH THEIR DIFFERENCES[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 662-675. doi: 10.11948/20210260

ENTIRE FUNCTIONS THAT SHARE A SET WITH THEIR DIFFERENCES

1.
Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China

Corresponding author: Email: mlfang@hdu.edu.cn(M. Fang)
Fund Project: This paper is supported by the NNSF of China(No. 12171127) and the NSF of Zhejiang Province (No. LY21A010012)

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 $\lambda(f)<\rho(f)<\infty$. 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 ([15]).
- Entire functions /
- exponent of convergence /
- unicity /
- differences
MSC: 30D35

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