| 曾翠萍,邓炳茂,方明亮.涉及分担函数与分担值的正规定则[J].数学年刊A辑,2021,42(1):115~124 |
| 涉及分担函数与分担值的正规定则 |
| Normal Criterion Concerning Shared Functions and Shared Values |
| Received:September 10, 2017 Revised:March 22, 2018 |
| DOI：10.16205/j.cnki.cama.2021.0010 |
| 中文关键词: 亚纯函数, 正规族, 分担函数, 分担值 |
| 英文关键词:Meromorphic functions, Normal families, Shared functions, Shared values |
| 基金项目:国家自然科学基金 (No.,11901119)和广东省普通高校特色创新类项目(No.,2019KTSCX111) |
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| 中文摘要: |
| 研究了涉及分担函数的正规定则, 证明了: 设mathcal{F}为定义在区域D内的一族亚纯函数,n, k是两个正整数, 满足ngeq k+3. 如果对于mathcal{F}中任意一个函数f,(f^n)^{(k)}-z 至多有一个不同的零点, 则mathcal{F}在D内正规. 此结论说明在(f^n)^{(k)}具有不动点的情形下,1990年杨乐在~Notre Dame~大学举行的学术会议上提出的断言仍然成立. |
| 英文摘要: |
| The authors study normal criterion concerning share functions and share values and prove: Let F be a family of meromorphic functions in D, and let k, n be two positive integers with n > k + 3. For each f ∈ F, (f n)(k) ? z has at most one zero, then F is normal in D. It means that the claim made by Yang at the academic conference in University of Notre Dame in 1990 is still valid when (f n)(k) has fixed point. |
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