Normal families of meromorphic functions whose poles are locally uniformly discrete

Authors

  • Liu Xiaoyi Department of Mathematics, Changshu Institute of Technology, Changshu

DOI:

https://doi.org/10.5556/j.tkjm.45.2014.1042

Abstract

Let $h$ be a positive number, and let $a(z)$ be a function holomorphic and zero-free on a domain $D$. Let $\mathcal{F}$ be a family of meromorphic functions on $D$ such that for every $f\in\mathcal{F}$, $f(z)=0\Rightarrow f'(z)=a(z)$ and $f'(z)=a(z)\Rightarrow{|f''(z)|\leq{h}}$. Suppose that each pair of functions $f$ and $g$ in $\mathcal{F}$ have the same poles. Then $\mathcal{F}$ is normal on $D$.

Author Biography

Liu Xiaoyi, Department of Mathematics, Changshu Institute of Technology, Changshu

Department of Mathematics, Changshu Institute of Technology, Changshu,Jiangsu 215500, P.R. China

References

J. M. Chang, M. L. Fang and L. Zalcman, Normal families of holomorphic functions, J. Math. Illinois. 48(2004), 319-337.

J. M. Chang, A note on normality of meromorphic functions, Proc. Japan Acad., 83, Ser. A(2007),60-62.

J. Clunie and W. K. Hayman, The spherical derivative of integral and meromorphic functions, Comment. Math. Helv. 40 (1966), 117-148.

W. K. Hayman, Meromorphic functions, Clarendon Press, Oxford,1964.

K. L. Hiong, Sur les fonctions holomorphes dont les derivees admettent une valeur exceptionnelle, Ann. Sci. ┬┤Ecole Norm. Sup. (3) 72 (1955), 165-197.

X. C. Pang and L. Zalcman, Normal families and shared values, Bull. London Math. Soc. 32 (2000), 325-331.

J. L. Schiff, Normal families, Springer-Verlag, New York, 1993.

W. Schwick, Sharing values and normality, Arch Math., 59(1993), 50-54.

L. Yang, Value distribution theory, Spring-Verlag, Berlin, 1993.

Downloads

Published

2014-03-27

How to Cite

Xiaoyi, L. (2014). Normal families of meromorphic functions whose poles are locally uniformly discrete. Tamkang Journal of Mathematics, 45(1), 13-19. https://doi.org/10.5556/j.tkjm.45.2014.1042

Issue

Section

Papers