Normal Criterion Concerning Shared Values

Wei Chen, Yingying Zhang, Jiwen Zeng and Honggen Tian

Journal of Applied Mathematics, 2012, vol. 2012, 1-7

Abstract:

We study normal criterion of meromorphic functions shared values, we obtain the following. Let F be a family of meromorphic functions in a domain D , such that function f ∈ F has zeros of multiplicity at least 2, there exists nonzero complex numbers b f , c f depending on f satisfying ( i ) b f / c f is a constant; ( i i ) min { σ ( 0 , b f ) , σ ( 0 , c f ) , σ ( b f , c f ) ≥ m } for some m > 0 ; ( i i i ) ( 1 / c f k - 1 ) ( f ′ ) k ( z ) + f ( z ) ≠ b f k / c f k - 1 or ( 1 / c f k - 1 ) ( f ′ ) k ( z ) + f ( z ) = b f k / c f k - 1 ⇒ f ( z ) = b f , then F is normal. These results improve some earlier previous results.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:312324

DOI: 10.1155/2012/312324

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