### Nonexceptional Functions and Normal Families of Zero-free Meromorphic Functions

#### Abstract

Let $k$ be a positive integer, let $\mathcal F$ be a family of zero-free meromorphic

functions in a domain $D$, all of whose poles are multiple, and let $h$ be a meromorphic

function in $D$, all of whose poles are simple, $h\not\equiv0, \infty$. If for each $f\in\mathcal F$,

$f^{(k)}(z)-h(z)$ has at most $k$ zeros in $D$, ignoring multiplicities,

then $\mathcal F$ is normal in $D$. The examples are

provided to show that the result is sharp.

#### Full Text:

PDF### Refbacks

- There are currently no refbacks.