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

Xiu-Min Zheng, and Hong-Yan Xu. "Results on the deficiencies of some differential-difference polynomials of meromorphic functions." Open Mathematics 14.1 (2016): 100-108. <http://eudml.org/doc/276899>.

@article{Xiu2016,
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 lim sup r→+∞ T(r, f) T(r,  f ′ ) <+∞, \[\mathop \{\lim \,\{\rm sup\}\}\limits \_\{r \rightarrow + \infty \} \{\{T(r,\,f)\} \over \{T(r,\,f^\{\prime \})\}\}\{\rm \{ < \}\} + \infty ,\] 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).},
author = {Xiu-Min Zheng, Hong-Yan Xu},
journal = {Open Mathematics},
keywords = {Meromorphic function; Differential-difference polynomial; Deficiency; meromorphic functions of finite order; differential difference polynomials},
language = {eng},
number = {1},
pages = {100-108},
title = {Results on the deficiencies of some differential-difference polynomials of meromorphic functions},
url = {http://eudml.org/doc/276899},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Xiu-Min Zheng
AU - Hong-Yan Xu
TI - Results on the deficiencies of some differential-difference polynomials of meromorphic functions
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 100
EP - 108
AB - 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 ′ ) <+∞, \[\mathop {\lim \,{\rm sup}}\limits _{r \rightarrow + \infty } {{T(r,\,f)} \over {T(r,\,f^{\prime })}}{\rm { < }} + \infty ,\] 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).
LA - eng
KW - Meromorphic function; Differential-difference polynomial; Deficiency; meromorphic functions of finite order; differential difference polynomials
UR - http://eudml.org/doc/276899
ER -