与零点个数有关的亚纯函数正规定则

Abstract

Abstract:

This paper considers normality criteria for a family of meromorphic functions concerning zero numbers. Let F be a family of meromorphic functions defined in a domain D, all of whose zeros and poles have multiplicity at least k and k+1 respectively, let m, n and k be three positive integers satisfying n≥m+2, and a(≠0), b be two finite constants. If for each function f∈F, f^(k)-afⁿ-b has at most m distinct zeros in D, then F is normal in D. Our results improve theorem 1 by Deng et al.^[18] and generalize the related theorems of Ye et al.^[16], Zhang et al.^[22] and Chen et al.^[19]. Meanwhile, some examples are given to show the sharpness of our results.

Key words: Meromorphic function, Zero numbers, Normal criterion

CLC Number:

O174.52

Wang Qiong, Chen Wei, Yuan Wenjun, Tian Honggen. Normality Criteria of Meromorphic Functions with Zero Numbers[J].Acta mathematica scientia,Series A, 2017, 37(1): 7-17.

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References

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Normality Criteria of Meromorphic Functions with Zero Numbers

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