Meromorphic Functions Sharing a Small Function
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 fn...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2007/60718 |
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| Summary: | 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 fnf′ and gng′ share a(z) CM, then either fn(z)f′(z)gn(z)g′(z)≡a2(z), or f(z)≡tg(z) for a constant satisfying tn+1=1. As applications, we give several examples. |
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| ISSN: | 1085-3375 1687-0409 |