Journal of Applied Mathematics

Normal Criterion Concerning Shared Values

Wei Chen, Yingying Zhang, Jiwen Zeng, and Honggen Tian

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 312324, 7 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495289

Digital Object Identifier
doi:10.1155/2012/312324

Mathematical Reviews number (MathSciNet)
MR2970426

Zentralblatt MATH identifier
1253.30046

Citation

Chen, Wei; Zhang, Yingying; Zeng, Jiwen; Tian, Honggen. Normal Criterion Concerning Shared Values. J. Appl. Math. 2012 (2012), Article ID 312324, 7 pages. doi:10.1155/2012/312324. https://projecteuclid.org/euclid.jam/1355495289


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