Abstract and Applied Analysis

Meromorphic Functions Sharing a Small Function

Songmin Wang and Zongsheng Gao

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2007 (2007), Article ID 60718, 6 pages.

Dates
First available in Project Euclid: 5 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1183666875

Digital Object Identifier
doi:10.1155/2007/60718

Mathematical Reviews number (MathSciNet)
MR2320797

Zentralblatt MATH identifier
1152.30030

Citation

Wang, Songmin; Gao, Zongsheng. Meromorphic Functions Sharing a Small Function. Abstr. Appl. Anal. 2007 (2007), Article ID 60718, 6 pages. doi:10.1155/2007/60718. https://projecteuclid.org/euclid.aaa/1183666875


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