Normal Families of Meromorphic Functions with Sharing Functions

Dan Liu ; Bingmao Deng ; Degui Yang

Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 3

Résumé

Let $\mathcal F$ be a family of meromorphic functions in a domain $D$, let $k$ be a positive integer, and let $h(z)(\not\equiv 0, \infty)$ be a meromorphic function in $D$ such that any $f\in \mathcal F$ have neither common zeros nor common poles with $h(z)$. If, for each $f \in \mathcal F$, the multiplicity of the zeros $f$ is at least $k$, and $f=0 \Leftrightarrow f^{(k)}=0$, and $f^{(k)}(z)=h(z)\Rightarrow f(z)=h(z)$, then $\mathcal F$ is normal in $D$. This improves the results due to Xia and Xu.

Détail

Classification : 30D45