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

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 100-108
- ISSN: 2391-5455

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topXiu-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 -

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