We proved： Let F be a family of meromorphic functions in a domain D anda α ≠0, b ∈C. If f1（z） - α（f（z））^2 ≠ b, f≠ 0 and the poles of f（z） are of multiplicity ≥ 3 foreach f（z） ∈F, then F is normal in D.
In this paper, we generalize an, inequality of meromorphic mappings to quasimeromorphic ones. Applying the results here, we can establish a normal criterion of quasimeromorphic mappings.
In this paper, we study the normality criteria of meromorphic functions concerning shared fixed-points, we obtain: Let F be a family of meromorphic functions defined in a domain D. Let n, k ≥ 2 be two positive intege...In this paper, we study the normality criteria of meromorphic functions concerning shared fixed-points, we obtain: Let F be a family of meromorphic functions defined in a domain D. Let n, k ≥ 2 be two positive integers. For every f ∈ F, all of whose zeros have multiplicity at least (nk+2)/(n-1). If f(f(k))nand g(g(k))nshare z in D for each pair of functions f and g, then F is normal.展开更多
In this paper, we consider normality criteria for a family of meromorphic functions concerning shared values. Let F be a family of meromorphic functions defined in a domain D, m, n, k and d be four positive integers s...In this paper, we consider normality criteria for a family of meromorphic functions concerning shared values. Let F be a family of meromorphic functions defined in a domain D, m, n, k and d be four positive integers satisfying m ≥ n ＋ 2 and d≥k＋1/m-n-1 and a（≠ 0）, b be two finite constants. Suppose that every f∈F has all its zeros and poles of multiplicity at least k and d, respectively. If （fn）（k）-afm and （gn）（k） -agm share the value b for every pair of functions （f, g） of ~, then is normal in D. Our results improve the related theorems of Schwick （Schwick W. Normality criteria for families of meromorphic function. J. Anal. Math., 1989, 52： 241-289）, Li and Gu （Li Y T, Gu Y X. On normal families of meromorphic functions. J. Math. Anal. Appl., 2009, 354： 421-425）.展开更多
In this paper, we study the normality of families of meromorohic functions related to a Hayman conjecture. We prove that the conditions in Hayman conjecture and in other criterions can be relaxed. The results in this ...In this paper, we study the normality of families of meromorohic functions related to a Hayman conjecture. We prove that the conditions in Hayman conjecture and in other criterions can be relaxed. The results in this paper improve some previous results.展开更多
In this article,we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values,which improves some earlier related results.
In this paper, we study the normal families related with a Hayman conjecture of higher derivative concerning zero numbers, and get one normal criteria.Our result improve some earlier related result.
In this paper, we obtain the following normal criterion： Let F be a family of mero-morphic functions in domain D belong to C, all of whose zeros have multiplicity k ＋ 1 at least. If there exist holomorphic functio...In this paper, we obtain the following normal criterion： Let F be a family of mero-morphic functions in domain D belong to C, all of whose zeros have multiplicity k ＋ 1 at least. If there exist holomorphic functions α（z） not vanishing on D, such that for every function f（z） ∈F, f（z） shares α（z） IM with L（f） on D, then F is normal on D, where L（f） is linear differential polynomials of f（z） with holomorphic coefficients, and k is some positive numbers. We also proved coressponding results on normal functions.展开更多
文摘We proved： Let F be a family of meromorphic functions in a domain D anda α ≠0, b ∈C. If f1（z） - α（f（z））^2 ≠ b, f≠ 0 and the poles of f（z） are of multiplicity ≥ 3 foreach f（z） ∈F, then F is normal in D.
基金the National Natural Science Foundation of China (No.198710 64 )
文摘In this paper, we generalize an, inequality of meromorphic mappings to quasimeromorphic ones. Applying the results here, we can establish a normal criterion of quasimeromorphic mappings.
文摘In this paper, we study the normality criteria of meromorphic functions concerning shared fixed-points, we obtain: Let F be a family of meromorphic functions defined in a domain D. Let n, k ≥ 2 be two positive integers. For every f ∈ F, all of whose zeros have multiplicity at least (nk+2)/(n-1). If f(f(k))nand g(g(k))nshare z in D for each pair of functions f and g, then F is normal.
文摘In this paper, we consider normality criteria for a family of meromorphic functions concerning shared values. Let F be a family of meromorphic functions defined in a domain D, m, n, k and d be four positive integers satisfying m ≥ n ＋ 2 and d≥k＋1/m-n-1 and a（≠ 0）, b be two finite constants. Suppose that every f∈F has all its zeros and poles of multiplicity at least k and d, respectively. If （fn）（k）-afm and （gn）（k） -agm share the value b for every pair of functions （f, g） of ~, then is normal in D. Our results improve the related theorems of Schwick （Schwick W. Normality criteria for families of meromorphic function. J. Anal. Math., 1989, 52： 241-289）, Li and Gu （Li Y T, Gu Y X. On normal families of meromorphic functions. J. Math. Anal. Appl., 2009, 354： 421-425）.
基金The NSF(11271090) of Chinathe NSF(S2012010010121) of Guangdong Provincethe Graduate Research and Innovation Projects(XJGRI2013131) of Xinjiang Province
文摘In this paper, we study the normality of families of meromorohic functions related to a Hayman conjecture. We prove that the conditions in Hayman conjecture and in other criterions can be relaxed. The results in this paper improve some previous results.
文摘In this article,we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values,which improves some earlier related results.
文摘In this paper, we study the normal families related with a Hayman conjecture of higher derivative concerning zero numbers, and get one normal criteria.Our result improve some earlier related result.
文摘1 .Introduetion Afteritiaing the ooncept of normal family of meromorphio funoions,P·Monteleotablsshod aniport criterion for norality.Let F be a family
基金the"11.5"Research & Study Programe of SWUST(No.06zx2116)
文摘In this paper, we obtain the following normal criterion： Let F be a family of mero-morphic functions in domain D belong to C, all of whose zeros have multiplicity k ＋ 1 at least. If there exist holomorphic functions α（z） not vanishing on D, such that for every function f（z） ∈F, f（z） shares α（z） IM with L（f） on D, then F is normal on D, where L（f） is linear differential polynomials of f（z） with holomorphic coefficients, and k is some positive numbers. We also proved coressponding results on normal functions.
