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Some further results on meromorphic functions that share two sets

Qi Han;  Hong-Xun Yi — 2008

Annales Polonici Mathematici

This paper concerns the uniqueness of meromorphic functions and shows that there exists a set S ⊂ ℂ of eight elements such that any two nonconstant meromorphic functions f and g in the open complex plane ℂ satisfying E 3 ) ( S , f ) = E 3 ) ( S , g ) and Ē(∞,f) = Ē(∞,g) are identical, which improves a result of H. X. Yi. Also, some other related results are obtained, which generalize the results of G. Frank, E. Mues, M. Reinders, C. C. Yang, H. X. Yi, P. Li, M. L. Fang and H. Guo, and others.

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

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.

On the uniqueness of an entire function sharing a small entire function with some linear differential polynomial

Xiao-Min Li;  Hong-Xun Yi — 2009

Czechoslovak Mathematical Journal

We prove a theorem on the growth of nonconstant solutions of a linear differential equation. From this we obtain some uniqueness theorems concerning that a nonconstant entire function and its linear differential polynomial share a small entire function. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible.

Uniqueness theorems for entire functions whose difference polynomials share a meromorphic function of a smaller order

Xiao-Min Li;  Wen-Li Li;  Hong-Xun Yi;  Zhi-Tao Wen — 2011

Annales Polonici Mathematici

We deal with uniqueness of entire functions whose difference polynomials share a nonzero polynomial CM, which corresponds to Theorem 2 of I. Laine and C. C. Yang [Proc. Japan Acad. Ser. A 83 (2007), 148-151] and Theorem 1.2 of K. Liu and L. Z. Yang [Arch. Math. 92 (2009), 270-278]. We also deal with uniqueness of entire functions whose difference polynomials share a meromorphic function of a smaller order, improving Theorem 5 of J. L. Zhang [J. Math. Anal. Appl. 367 (2010), 401-408], where the entire...

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