Abstract
In this article, we deduce a uniqueness result of entire functions that share a small entire function with their two difference operators, generalizing some previous theorems of (Farissi et al. in Complex Anal. Oper. Theory 10:1317-1327, 2015, Theorem 1.1) and (Chen and Li in Adv. Differ. Equ. 2014:311, 2014, Theorem 1.1) by omitting the assumption that the shared small entire function is periodic.
Highlights
1 Introduction and main result Nevanlinna theory of value distributions is concerned with the density of points where a meromorphic function takes a certain value in the complex plane
Many papers have been devoted to the investigation of the uniqueness problems related to meromorphic functions and their shifts or their difference operators and one got a lot of results
We find that the shared small function a(z) is a periodic function with period c
Summary
Introduction and main resultNevanlinna theory of value distributions is concerned with the density of points where a meromorphic function takes a certain value in the complex plane. Denote the set of all the small functions of f (z) by S(f ). Let f (z) and g(z) be two meromorphic functions and let a(z) be a small entire function of f (z) and g(z). Chen et al [ , ] investigated two uniqueness problems on entire functions that share a small periodic entire function with their two difference operators as follows.
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