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

• Autorzy: Xiu-Min Zheng , Hong-Yan Xu
• Języki publikacji: EN

Abstrakty

EN

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 lim sup r→+∞ T(r, f) T(r,  f ′ ) <+∞, $$\mathop {\lim \,{\rm sup}}\limits_{r \to + \infty } {{T(r,\,f)} \over {T(r,\,f')}}{\rm{ < }} + \infty ,$$ 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).

Słowa kluczowe

EN

Meromorphic function; Differential-difference polynomial; Deficiency

Kategorie tematyczne

• 39A10: Difference equations, additive
• 30D35: Distribution of values, Nevanlinna theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 100-108

Daty

wydano

2016-01-01

otrzymano

2015-08-28

zaakceptowano

2015-11-24

online

2016-02-24

Twórcy

autor

Xiu-Min Zheng

• Institute of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi, 330022,

autor

Hong-Yan Xu

• Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen, Jiangxi, 333403,

Identyfikatory

DOI

10.1515/math-2016-0009