On normal families and differential polynomials for meromorphic functions |
| |
Authors: | Qian Lu |
| |
Affiliation: | Department of Mathematics, Southwest University of Science and Technology, Mianyang, Sichuan 621010, PR China |
| |
Abstract: | We consider the normality criterion for a families F meromorphic in the unit disc Δ, and show that if there exist functions a(z) holomorphic in Δ, a(z)≠1, for each z∈Δ, such that there not only exists a positive number ε0 such that |an(a(z)−1)−1|?ε0 for arbitrary sequence of integers an(n∈N) and for any z∈Δ, but also exists a positive number B>0 such that for every f(z)∈F, B|f′(z)|?|f(z)| whenever f(z)f″(z)−a(z)(f′2(z))=0 in Δ. Then is normal in Δ. |
| |
Keywords: | Differential polynomials Meromorphic functions Zeros Normality |
本文献已被 ScienceDirect 等数据库收录! |
|