On normal families and differential polynomials for meromorphic functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:340

Article

Lu, Qian

关键词: differential polynomials;    meromorphic functions;    zeros;    normality;   

DOI  :  10.1016/j.jmaa.2007.08.038

来源: Elsevier

【 摘 要 】

We consider the normality criterion for a families F meromorphic in the unit disc Delta, and show that if there exist functions a (z) holomorphic in Delta, a(z) not equal 1, for each z epsilon Delta, such that there not only exists a positive number epsilon(0) such that vertical bar a(n) (a(z) - 1) - 1 vertical bar >= epsilon(0) for arbitrary sequence of integers a(n) (n epsilon N) and for any z epsilon Delta, but also exists a positive number B > 0 such that for every f (z) epsilon F, B vertical bar f'(z)vertical bar <= vertical bar f(z)vertical bar whenever f(z) f ''(z) - a(z)(f'(z))(2) = 0 in Delta. Then {f'(z)/f(z): f(z) epsilon F} is normal in Delta.

【 授权许可】

Free