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2007 Meromorphic Functions Sharing a Small Function
Songmin Wang, Zongsheng Gao
Abstr. Appl. Anal. 2007: 1-6 (2007). DOI: 10.1155/2007/60718

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.

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Songmin Wang. Zongsheng Gao. "Meromorphic Functions Sharing a Small Function." Abstr. Appl. Anal. 2007 1 - 6, 2007. https://doi.org/10.1155/2007/60718

Information

Published: 2007
First available in Project Euclid: 5 July 2007

zbMATH: 1152.30030
MathSciNet: MR2320797
Digital Object Identifier: 10.1155/2007/60718

Rights: Copyright © 2007 Hindawi

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