학술논문
On the value distribution of $f^2f^{(k)}$.
Document Type
Journal
Author
Huang, Xiaojun (PRC-SUN-M) AMS Author Profile; Gu, Yongxing (PRC-CHQG) AMS Author Profile
Source
Subject
30 Functions of a complex variable -- 30D Entire and meromorphic functions, and related topics
30D45Bloch functions, normal functions, normal families
30D45
Language
English
Abstract
Let $f(z)$ be a transcendental meromorphic function in $|z|<\infty$ and let $k$ be a positive integer. Then the authors prove the inequality $$T(r,f)<6N(r,1/(f^2f^{(k)}-1))+S(r,f)\tag1$$ and give a sufficient condition for a family of meromorphic functions in a domain to be normal as an application of the inequality (1). The inequality (1) is a generalization of the inequality for $k=1$ proved by Q. D. Zhang in 1992.