Normality criteria and multiple values II

Volume 102 / 2011

Yan Xu, Jianming Chang Annales Polonici Mathematici 102 (2011), 91-99 MSC: Primary 30D05; Secondary 30D45. DOI: 10.4064/ap102-1-9

Abstract

Let $\cal F$ be a family of meromorphic functions defined in a domain $D$, let $\psi$ $(\not\equiv 0, \infty)$ be a meromorphic function in $D$, and $k$ be a positive integer. If, for every $f\in \cal F$ and $z\in D$, (1) $f\neq 0$, $f^{(k)}\neq 0$; (2) all zeros of $f^{(k)}-\psi$ have multiplicities at least $(k+2)/k$; (3) all poles of $\psi$ have multiplicities at most $k$, then $\cal F$ is normal in $D$.

Authors

  • Yan XuInstitute of Mathematics
    School of Mathematics
    Nanjing Normal University
    Nanjing 210046, P.R. China
    e-mail
  • Jianming ChangDepartment of Mathematics
    Changshu Institute of Technology
    Changshu, Jiangsu, 215500, P.R. China
    e-mail

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