## A new normal criterion and its application.(Chinese)Zbl 0766.30029

The author first shows (Theorem 1) that if $$f$$ is an entire function, $$n\geq 2$$ and $$x\geq 0$$ are two integers, $$a\neq 0$$ such that $$f^{(k)}+af^ n\neq 0$$, then $$f\equiv$$constant. This result was then used to prove that for a non-negative integer $$k$$, $$n$$ integer $$\geq 2$$, and $$a$$, $$b$$ two finite complex numbers with $$a\neq 0$$, the set of all functions $$f$$ that are holomorphic in a domain $$D$$ satisfying, in $$D$$, $$f^{(k)}+af^ n\neq b$$ is a normal family.
Reviewer’s note: Theorem 1 follows immediately by applying the Tumura- Clunie type of the theorem [cf. W. K. Hayman’s book “Meromorphic functions” (1964; Zbl 0115.062), p. 69]. Thus if $$f$$ is entire and satisfies $$f'+af^ 2\neq b$$ (for some constants $$a\neq 0,b$$), then $$f$$ must be a constant not just has an order $$\leq 2$$ as asserted in the lemma 5 of the paper.

### MSC:

 30D45 Normal functions of one complex variable, normal families 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory

### Keywords:

differential polynomials; Riccati equation; normal family

### Citations:

Zbl 0149.030; Zbl 0115.062