与对数导数相关的正规定则
Normal Criterion Related to LogarithmicDerivatives
DOI: 10.12677/PM.2024.147284, PDF, 下载: 4  浏览: 12  国家自然科学基金支持
作者: 古丽术热•吐尔逊, 杨锦华*：新疆师范大学数学科学学院，新疆 乌鲁木齐
关键词: 亚纯函数；正规定则；对数导数；Meromorphic Function； Normal Criterion； Logarithmic Derivatives Copyright
摘要: 文章利用 Zalcman-Pang 引理，结合对数导数函数族正规，对满足条件 f′(z) − a(z)fk(z) ≠ b(z) 的亚纯函数族的正规性进行研究。本文得到当 k = 2 且例外函数 a(z)、b(z) 均为全纯函数时，在函数族零点、极点均重级的条件下，亚纯函数族是正规的。
Abstract: This paper studies the regularity of the meromorphic function family satisfying the condition f′(z) − a(z)fk(z) ≠ b(z) by using the P-Z lemma and combining the normalization of logarithmic derivative family. This paper obtains that when k = 2 and omitted functions a(z) and b(z) are holomorphic functions, under the condition of zero and pole weight of the function family, the meromorphic function family is normal.
文章引用：古丽术热•吐尔逊, 杨锦华. 与对数导数相关的正规定则[J]. 理论数学, 2024, 14(7): 173-180. https://doi.org/10.12677/PM.2024.147284

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