## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Normal families and shared values of meromorphic functions

#### Abstract

Let $\cal{F}$ be a family of meromorphic functions in a domain $D$, let $q, k$ be two positive integers, and let $a, b$ be two non-zero complex numbers. If, for each $f \in \cal {F}$, the zeros of $f$ have multiplicity at least $k+1$, and $f=a \Leftrightarrow G(f)=b$, where $G(f)=P(f^{(k)})+H(f)$ be a differential polynomial of $f$ satisfying $q \geq \gamma_H$, and $\frac{\Gamma}{\gamma} |_H < k+1$, then $\cal {F}$ is normal in $D$.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 83, Number 3 (2007), 36-39.

Dates
First available in Project Euclid: 9 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1176126888

Digital Object Identifier
doi:10.3792/pjaa.83.36

Mathematical Reviews number (MathSciNet)
MR2317308

Zentralblatt MATH identifier
1179.30033

Subjects
Primary: 30D45: Bloch functions, normal functions, normal families

#### Citation

Lei, Chunlin; Fang, Mingliang; Yang, Degui. Normal families and shared values of meromorphic functions. Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 3, 36--39. doi:10.3792/pjaa.83.36. https://projecteuclid.org/euclid.pja/1176126888

#### References

• W. Schwick, Sharing values and normality, Arch. Math. (Basel) 59 (1992), no. 1, 50–54.
• M. Fang, A note on sharing values and normality, J. Math. Study 29 (1996), no. 4, 29–32.
• M. Fang and L. Zalcman, Normal families and shared values of meromorphic functions. III, Comput. Methods Funct. Theory 2 (2002), no. 2, 385–395.
• X. Pang and L. Zalcman, Normal families and shared values, Bull. London Math. Soc. 32 (2000), no. 3, 325–331.
• Y. Wang and M. Fang, Picard values and normal families of meromorphic functions with multiple zeros, Acta Math. Sinica (N.S.) 14 (1998), no. 1, 17–26.