scholarly journals On Value Distribution of Difference Polynomials of Meromorphic Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Zong-Xuan Chen
Keyword(s):  
Meromorphic Functions ◽  
Value Distribution ◽  
Difference Analogue ◽  
Difference Polynomials ◽  
The Difference

We study the value distribution of the difference counterpartΔf(z)−af(z)noff′(z)−af(z)nand obtain an almost direct difference analogue of results of Hayman.

scholarly journals Difference Equations and Sharing Values Concerning Entire Functions and Their Difference

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhiqiang Mao ◽  
Huifang Liu
Keyword(s):  
Difference Equations ◽  
Entire Functions ◽  
Value Distribution ◽  
Difference Operators ◽  
Sharing Values ◽  
Difference Analogue ◽  
The Difference ◽  
Brück Conjecture

The value distribution of solutions of certain difference equations is investigated. As its applications, we investigate the difference analogue of the Brück conjecture. We obtain some results on entire functions sharing a finite value with their difference operators. Examples are provided to show that our results are the best possible.

Some results for complex partial q-difference equations in ℂ n \mathbb{C}^{n}

2019 ◽  
Vol 26 (3) ◽  
pp. 471-481
Author(s):  
Yue Wang
Keyword(s):  
Difference Equations ◽  
Nevanlinna Theory ◽  
Meromorphic Functions ◽  
Zero Order ◽  
Value Distribution ◽  
Meromorphic Solutions ◽  
Difference Polynomials

Abstract Using the Nevanlinna theory of the value distribution of meromorphic functions, the value distribution of complex partial q-difference polynomials of meromorphic functions of zero order is investigated. The existence of meromorphic solutions of some types of systems of complex partial q-difference equations in {\mathbb{C}^{n}} is also investigated. Improvements and extensions of some results in the literature are presented. Some examples show that our results are, in a certain sense, the best possible.

scholarly journals On the Deficiencies of Some Differential-Difference Polynomials

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Xiu-Min Zheng ◽  
Hong Yan Xu
Keyword(s):  
Value Distribution ◽  
Characteristic Functions ◽  
Difference Analogue ◽  
Difference Polynomials

The characteristic functions of differential-difference polynomials are investigated, and the result can be viewed as a differential-difference analogue of the classic Valiron-Mokhon’ko Theorem in some sense and applied to investigate the deficiencies of some homogeneous or nonhomogeneous differential-difference polynomials. Some special differential-difference polynomials are also investigated and these results on the value distribution can be viewed as differential-difference analogues of some classic results of Hayman and Yang. Examples are given to illustrate our results at the end of this paper.

scholarly journals Results on the deficiencies of some differential-difference polynomials of meromorphic functions

2016 ◽  
Vol 14 (1) ◽  
pp. 100-108 ◽  
Author(s):  
Xiu-Min Zheng ◽  
Hong-Yan Xu
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Meromorphic Functions ◽  
Value Distribution ◽  
Small Function ◽  
Complex Constant ◽  
Difference Polynomials

Abstract In this paper, we study the relation between the deficiencies concerning a meromorphic function f(z), its derivative f′(z) and differential-difference monomials f(z)mf(z+c)f′(z), f(z+c)nf′(z), f(z)mf(z+c). The main results of this paper are listed as follows: Let f(z) be a meromorphic function of finite order satisfying $$\mathop {\lim \,{\rm sup}}\limits_{r \to + \infty } {{T(r,\,f)} \over {T(r,\,f')}}{\rm{ < }} + \infty ,$$ and c be a non-zero complex constant, then δ(∞, f(z)m f(z+c)f′(z))≥δ(∞, f′) and δ(∞,f(z+c)nf′(z))≥ δ(∞, f′). We also investigate the value distribution of some differential-difference polynomials taking small function a(z) with respect to f(z).

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