Value distribution of general differential-difference polynomials of meromorphic functions

2018 ◽  
Vol 27 (4) ◽  
pp. 931-942 ◽  
Author(s):  
Renukadevi S. Dyavanal ◽  
Madhura M. Mathai
Keyword(s):  
Meromorphic Functions ◽  
Value Distribution ◽  
Difference Polynomials

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.

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 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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