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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| _version_ | 1850235261472997376 |
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| author | Songmin Wang Zongsheng Gao |
| author_facet | Songmin Wang Zongsheng Gao |
| author_sort | Songmin Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1b1e5af113124cda89d3b9d77c3baa91 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1b1e5af113124cda89d3b9d77c3baa912025-08-20T02:02:20ZengWileyAbstract and Applied Analysis1085-33751687-04092007-01-01200710.1155/2007/6071860718Meromorphic Functions Sharing a Small FunctionSongmin Wang0Zongsheng Gao1LMIB and Department of Mathematics, Beihang University, Beijing 100083, ChinaLMIB and Department of Mathematics, Beihang University, Beijing 100083, ChinaWe 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.http://dx.doi.org/10.1155/2007/60718 |
| spellingShingle | Songmin Wang Zongsheng Gao Meromorphic Functions Sharing a Small Function Abstract and Applied Analysis |
| title | Meromorphic Functions Sharing a Small Function |
| title_full | Meromorphic Functions Sharing a Small Function |
| title_fullStr | Meromorphic Functions Sharing a Small Function |
| title_full_unstemmed | Meromorphic Functions Sharing a Small Function |
| title_short | Meromorphic Functions Sharing a Small Function |
| title_sort | meromorphic functions sharing a small function |
| url | http://dx.doi.org/10.1155/2007/60718 |
| work_keys_str_mv | AT songminwang meromorphicfunctionssharingasmallfunction AT zongshenggao meromorphicfunctionssharingasmallfunction |