摘要
对Frank-Weissenborn不等式中导数f^((k))能否被替换成一般的线性微分多项式a_0f+a_1f′+…+a_kf^((k))进行了研究,并彻底解决了这一问题.作为此结果的应用,Hayman-Yang不等式等几个已有的定理也得到了推广.例子表明,本文所得到的几个不等式的条件是基本的.
We study whether the derivative f^（k） in Frank-Weissenborn inequality can be replaced by a general linear differential polynomial α0f ＋ α1f′ ＋…＋ αkf^（k） or not, and have solvedit completely. As applications of this result, Hayman-Yang inequality and some known theorems are generalized. Examples are provided to show that the conditions of theorems obtained in the present paper are essential.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2008年第3期571-578,共8页
Acta Mathematica Sinica：Chinese Series
基金
陕西省教育厅专项科研基金(04JK127)
关键词
亚纯函数
线性微分多项式
零点
极点
meromorphic function
differential polynomial
zero
pole
