Let f be a transcendental meromorphic function and $g (z) = f (z + c ₁) + \dots + f (z + c_{k}) - k f (z)$ and $g_{k} (z) = f (z + c ₁) \dots f (z + c_{k}) - f^{k} (z)$ . A number of results are obtained concerning the exponents of convergence of the zeros of g(z), $g_{k} (z)$ , g(z)/f(z), and $g_{k} (z) / f^{k} (z)$ .

Uniqueness theorems and normal families of entire functions and their derivatives

Feng Lü; Junfeng Xu; Hongxun Yi — 2009

Annales Polonici Mathematici

We use the theory of normal families to obtain some uniqueness theorems for entire functions, which improve and generalize the related results of Rubel and Yang, and Li and Yi. Some examples are provided to show the sharpness of our results.

Hyper-order and order of meromorphic functions sharing functions

Jianming Qi; Wenjun Yuan; Hongxun Yi — 2015

Annales Polonici Mathematici

In this paper we mainly estimate the hyper-order of an entire function which shares one function with its derivatives. Some examples are given to show that the conclusions are meaningful.

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