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Unicity theorems for meromorphic functions that share three values

100%
Lü W.-R., Yi H.-X.
Annales Polonici Mathematici
|
2003
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tom 81
|
nr 2
131-138
EN
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.
2
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Uniqueness of meromorphic functions sharing a meromorphic function of a smaller order with their derivatives

100%
Li X.-M., Yi H.-X.
Annales Polonici Mathematici
|
2010
|
tom 98
|
nr 3
207-219
EN
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.
3
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Some further results on meromorphic functions that share two sets

100%
Han Q., Yi H.-X.
Annales Polonici Mathematici
|
2008
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tom 93
|
nr 1
17-31
EN
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.
4
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Results on weighted sharing of values for meromorphic functions

100%
Li X.-M., Yi H.-X.
Annales Polonici Mathematici
|
2007
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tom 92
|
nr 1
55-67
EN
We prove some results on uniqueness of functions with three shared values. Our results improve those given by H. X. Yi, I. Lahiri, T. C. Alzahary & H. X. Yi, and other authors.
5
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On uniqueness of meromorphic functions sharing three values and a set consisting of two small meromorphic functions

100%
Li X.-M., Yi H.-X.
Annales Polonici Mathematici
|
2009
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tom 96
|
nr 1
1-23
EN
We deal with a uniqueness theorem of two meromorphic functions that share three values with weights and also share a set consisting of two small meromorphic functions. Our results improve those by G. Brosch, I. Lahiri & P. Sahoo, T. C. Alzahary & H. X. Yi, P. Li & C. C. Yang, and others.
6
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Uniqueness theorems for entire functions whose difference polynomials share a meromorphic function of a smaller order

81%
Li X.-M., Li W.-L., Yi H.-X., Wen Z.-T.
Annales Polonici Mathematici
|
2011
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tom 102
|
nr 2
111-127
EN
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 functions are of finite orders.
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