Normal Criterion Concerning Shared Values. (6th September 2012) - Chen, Wei; Zhang, Yingying; Zeng, Jiwen; Tian, Honggen
Abstract : We study normal criterion of meromorphic functions shared values, we obtain the following. LetF be a family of meromorphic functions in a domainD, such that functionf ∈ F has zeros of multiplicity at least 2, there exists nonzero complex numbersb f, c f depending onf 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 somem > 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, thenF is normal. These results improve some earlier previous results.