Value distribution of meromorphic functions concerning differences

IF 1.4 3区 数学 Q1 MATHEMATICS
Zhiying He, Ge Wang, Mingliang Fang
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引用次数: 0

Abstract

In this paper, we study value distribution of meromorphic functions concerning differences and mainly prove the following result: Let f be a transcendental meromorphic function of \(1 \le \rho (f) < \infty \), let c be a nonzero constant, n a positive integer, and let P, Q be two polynomials. If \(\max \left\{ \lambda (f-P), \lambda \left( \frac{1}{f}\right) \right\} <\rho (f)\) and \(\Delta _{c}^{n}f \not \equiv 0\), then we have (i) \(\delta (Q, \Delta _c^n f)=0\) and \(\lambda (\Delta _{c}^{n}f-Q)=\rho (f)\), for \(\Delta _{c}^{n}P\not \equiv Q\); (ii) \(\delta (Q, \Delta _c^n f)=1\) and \(\lambda (\Delta _{c}^{n}f-Q)<\rho (f)\), for \(\Delta _{c}^{n}P\equiv Q\). The results obtained in this paper extend and improve some results due to Chen-Shon[J Math Anal Appl 2008], [Sci China Ser A 2009], Liu[Rocky Mountain J Math 2011], Cui-Yang[Acta Math Sci Ser B 2013], Chen[Complex Var Elliptic Equ 2013], Wang-Liu-Fang[Acta Math. Sinica (Chinese Ser) 2016].

关于差分的分形函数的值分布
在本文中,我们研究了有关差分的微变函数的值分布,并主要证明了以下结果:设 f 是一个超越欧几里得函数(1 \le \rho (f) < \infty \),设 c 是一个非零常数,n 是一个正整数,设 P, Q 是两个多项式。如果(\max \left\{ \lambda (f-P), \lambda \left( \frac{1}{f}\right) \right\} <;\(i) \(\delta (Q, \Delta _c^n f)=0\) and \(\lambda (\Delta _{c}^{n}f-Q)=\rho (f)\), for \(\Delta _{c}^{n}P not \equiv Q\);(ii) \(\delta (Q, \Delta _c^n f)=1\) and\(\lambda (\Delta _{c}^{n}f-Q)<\rho (f)\), for\(\Delta _{c}^{n}Pequiv Q\).本文所得到的结果扩展并改进了Chen-Shon[J Math Anal Appl 2008]、[Sci China Ser A 2009]、Liu[Rocky Mountain J Math 2011]、Cui-Yang[Acta Math Sci Ser B 2013]、Chen[Complex Var Elliptic Equ 2013]、Wang-Liu-Fang[Acta Math. Sinica (Chinese Ser) 2016]的一些结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Analysis and Mathematical Physics
Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
2.70
自引率
0.00%
发文量
122
期刊介绍: Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.
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