Displaying similar documents to “Some properties of solutions of complex q-shift difference equations”

Meromorphic solutions of q-shift difference equations

Kai Liu, Xiao-Guang Qi (2011)

Annales Polonici Mathematici

Similarity:

We establish a q-shift difference analogue of the logarithmic derivative lemma. We also investigate the value distributions of q-shift difference polynomials and the growth of solutions of complex q-shift difference equations.

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

Xiu-Min Zheng, Hong-Yan Xu (2016)

Open Mathematics

Similarity:

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 ′ ) <+∞, 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...

Uniqueness of meromorphic functions sharing a meromorphic function of a smaller order with their derivatives

Xiao-Min Li, Hong-Xun Yi (2010)

Annales Polonici Mathematici

Similarity:

We prove some uniqueness theorems for meromorphic functions and their derivatives that share a meromorphic function whose order is less than those of the above meromorphic functions. The results in this paper improve those given by G. G. Gundersen & L. Z. Yang, J. P. Wang, J. M. Chang & Y. Z. Zhu, and others. Some examples are provided to show that our results are the best possible.

Unicity theorems for meromorphic functions that share three values

Wei-Ran Lü, Hong-Xun Yi (2003)

Annales Polonici Mathematici

Similarity:

We deal with the problem of uniqueness of meromorphic functions sharing three values, and obtain several results which improve and extend some theorems of M. Ozawa, H. Ueda, H. X. Yi and other authors. We provide examples to show that results are sharp.