Normality Criteria for Families of Meromorphic Function Concerning Shared Values

Jianming Qi ; Jie Ding ; Lianzhong Yang

Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 2

Résumé

Let $k$ be a positive integer and let $\mathcal{F}$ be a family of meromorphic functions in the plane domain $D$ all of whose zeros with multiplicity at least $k$. Let $P=a_pz^p+\cdots+a_2z^2+z$ be a polynomial, $a_p,a_2\neq0$ and $p=\deg(P)\geq k+2$. If, for each $f,g\in \mathcal{F}$, $P(f)G(f)$ and $P(g)G(g)$ share a non-zero constant $b$ in $D$, where $G(f)=f^{(k)}+H(f)$ be a differential polynomial of $f$ satisfying $\frac{w}{\deg}|_H\leq \frac{k}{l+1}+1$ or $w(H)-\deg(H)$, then $\mathcal{F}$ is normal in $D$.

Détail

Classification : 30D35, 30D45.