Normality Criteria of Meromorphic Functions That Share a Holomorphic Function
Let F be a family of meromorphic functions defined in D, let ψ(≢0), a0,a1,...,ak-1 be holomorphic functions in D, and let k be a positive integer. Suppose that, for every function f∈F, f≠0, P(f)=f(k)+ak-1f(k-1)+⋯+a1f'+a0f≠0 and, for every pair functions (f,g)∈F, P(f), P(g) share ψ, then F is no...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/582854 |
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| author | Jie Ding Jianming Qi Taiying Zhu |
| author_facet | Jie Ding Jianming Qi Taiying Zhu |
| author_sort | Jie Ding |
| collection | DOAJ |
| description | Let F be a family of meromorphic functions defined in D, let ψ(≢0), a0,a1,...,ak-1 be holomorphic functions in D, and let k be a positive integer. Suppose that, for every function f∈F, f≠0, P(f)=f(k)+ak-1f(k-1)+⋯+a1f'+a0f≠0 and, for every pair functions (f,g)∈F, P(f), P(g) share ψ, then F is normal in D. |
| format | Article |
| id | doaj-art-d6282b8c9e0545d78c80ac6fdda50420 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d6282b8c9e0545d78c80ac6fdda504202025-02-03T05:58:53ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/582854582854Normality Criteria of Meromorphic Functions That Share a Holomorphic FunctionJie Ding0Jianming Qi1Taiying Zhu2School of Mathematics, Shandong University, Jinnan 250100, ChinaDepartment of Mathematics and Physics, Shanghai Dianji University, Shanghai 201306, ChinaDepartment of Mathematics and Physics, Shanghai Dianji University, Shanghai 201306, ChinaLet F be a family of meromorphic functions defined in D, let ψ(≢0), a0,a1,...,ak-1 be holomorphic functions in D, and let k be a positive integer. Suppose that, for every function f∈F, f≠0, P(f)=f(k)+ak-1f(k-1)+⋯+a1f'+a0f≠0 and, for every pair functions (f,g)∈F, P(f), P(g) share ψ, then F is normal in D.http://dx.doi.org/10.1155/2012/582854 |
| spellingShingle | Jie Ding Jianming Qi Taiying Zhu Normality Criteria of Meromorphic Functions That Share a Holomorphic Function Abstract and Applied Analysis |
| title | Normality Criteria of Meromorphic Functions That Share a Holomorphic Function |
| title_full | Normality Criteria of Meromorphic Functions That Share a Holomorphic Function |
| title_fullStr | Normality Criteria of Meromorphic Functions That Share a Holomorphic Function |
| title_full_unstemmed | Normality Criteria of Meromorphic Functions That Share a Holomorphic Function |
| title_short | Normality Criteria of Meromorphic Functions That Share a Holomorphic Function |
| title_sort | normality criteria of meromorphic functions that share a holomorphic function |
| url | http://dx.doi.org/10.1155/2012/582854 |
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