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 ′ ) <+∞, 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).
@article{bwmeta1.element.doi-10_1515_math-2016-0009,
author = {Xiu-Min Zheng and Hong-Yan Xu},
title = {Results on the deficiencies of some differential-difference polynomials of meromorphic functions},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {100-108},
zbl = {1351.30017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0009}
}
Xiu-Min Zheng; Hong-Yan Xu. Results on the deficiencies of some differential-difference polynomials of meromorphic functions. Open Mathematics, Tome 14 (2016) pp. 100-108. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0009/