Meromorphic Functions Sharing a Small Function

Songmin Wang and Zongsheng Gao

Abstract and Applied Analysis, 2007, vol. 2007, 1-6

Abstract:

We will study meromorphic functions that share a small function, and prove the following result: let f ( z ) and g ( z ) be two transcendental meromorphic functions in the complex plane and let n ≥ 11 be a positive integer. Assume that a ( z ) ( ≢ 0 ) is a common small function with respect to f ( z ) and g ( z ) . If f n f ′ and g n g ′ share a ( z ) CM, then either f n ( z ) f ′ ( z ) g n ( z ) g ′ ( z ) ≡ a 2 ( z ) , or f ( z ) ≡ t g ( z ) for a constant satisfying t n + 1 = 1 . As applications, we give several examples.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:060718

DOI: 10.1155/2007/60718

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