A positive answer for \(3\mathrm{IM}+1\mathrm{CM}\) problem with a general difference polynomial
type: Item
instance of: scholarly article
title: A positive answer for \(3\mathrm{IM}+1\mathrm{CM}\) problem with a general difference polynomial
zbMATH Open document ID: 1486.30100
DOI: 10.1155/2021/7113065
author: Huicai Xu
author: Shugui Kang
author: Qingcai Zhang
published in: Discrete Dynamics in Nature and Society
publication date: 2021-12-13T00:00:00Z
review text: Summary: In this paper, the \(3\mathrm{IM}+1\mathrm{CM}\) theorem with a general difference polynomial \(L(z, f)\) will be established by using new methods and technologies. Note that the obtained result is valid when the sum of the coefficient of \(L(z, f)\) is equal to zero or not. Thus, the theorem with the condition that the sum of the coefficient of \(L(z, f)\) is equal to zero is also a good extension for recent results. However, it is new for the case that the sum of the coefficient of \(L(z, f)\) is not equal to zero. In fact, the main difficulty of proof is also from this case, which causes the traditional theorem invalid. On the other hand, it is more interesting that the nonconstant finite-order meromorphic function \(f\) can be exactly expressed for the case \(f\equiv-L(z,f)\). Furthermore, the sharpness of our conditions and the existence of the main result are illustrated by examples. In particular, the main result is also valid for the discrete analytic functions.
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30D30
Mathematics Subject Classification ID: 39A05
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 39B32
zbMATH DE Number: 7443964
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/7113065
OpenAlex ID: W3216282294
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description: scientific article; zbMATH DE number 7443964