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Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (4): 691-697.

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On Miranda's Normality Criterion

ZENG Cui-Ping¹, LEI Chun-Lin², YANG De-Gui²

1.Department of Mathematics, Guangdong University of Finance, Guangzhou 510521|2.Department of Mathematics, South China
Agricultural University, Guangzhou 510642

Received:2010-02-08 Revised:2011-05-09 Online:2012-08-25 Published:2012-08-25
Supported by:
国家自然科学基金(11071083, 11101290)和广东省科技计划项目(2008B080701005)资助

Let F be a family of holomorphic functions in a domain D, L(f)=a_kf ^(k)+a_k_-1f ^(k-1)+…+a₁f'+a₀f, where a₀, a₁, …, a_k(≠0) are constants, and a, b, c be complex numbers with c≠0, a₀a≠b. If, for each f ∈F, f=a ↔L(f)=b, and f'=L'(f)=c whenever f =a, then F is normal in D. This improves Miranda's normality criterion.

Key words: Normal families, Meromorphic functions, Shared values

CLC Number:

30D45

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ZENG Cui-Ping, LEI Chun-Lin, YANG De-Gui. On Miranda's Normality Criterion[J].Acta mathematica scientia,Series A, 2012, 32(4): 691-697.

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