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On the Normal Meromorphic Functions

Zhu, Rongping, and Xu, Yan, (2007) On the Normal Meromorphic Functions. Bulletin of the Malaysian Mathematical Sciences Society, 30 (2). pp. 129-133. ISSN 0126-6705

Full text not available from this repository.

Official URL: http://math.usm.my/bulletin/pdf/v30n2/v30n2p5.pdf

Affiliations

Jiangsu University, Dept. of Mathematics
Nanjing Normal University, Dept. of Mathematics

Abstract

Let $\mathcal{F}$ be a family of functions meromorphic in D such that all the zeros of $f \in \mathcal{F}$ are of multiplicity at least $k$ (a positive integer), and let $E$ be a set containing $k + 4$ points of the extended complex plane. If, for each function $f \in \mathcal{F}$, there exists a constant $M$ and such that $(1-|z|^{2})^{k}|f^{(k)}(z)|1+|f(z)|^{k+1})\leq M$ whenever $z \in \{ f(z)\in E,z \in D \}$, then $\mathcal{F}$ is a uniformly normal family in $D$, that is, sup$\{ (1 — |z|^{2})f^{\sharp }(z) : z \in D, f \in \mathcal{F} \} < \infty$.


2000 Mathematics Subject Classification: 30D45, 30D35

Item Type:Journal
Keywords:Meromorphic function, Normal family, Normal function, Uniformly normal family.
Subjects:Q Science, Computer Science
ID Code:1455

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[2] W.K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.

[3] P. Lappan, The spherical derivative and normal functions, Ann. Acad. Sci. Penn. Ser. A I Math. 3(1977), 301—310.

[4] 0. Lehto and K. Virtanen, Boundary behavior and normal meromorphic functions, Acta Math. 97(1957), 47—56.

[5] X.C. Pang, Normal families and normal functions of meromorphic functions, Chinese Ann. of Math. 21(5)(2000), 601—604.

[6] Y. Xu, Normal functions and α-normal functions, Acta Math. Sinica, English Series 16(3)(2000), 399—404.

[7] L. Yang, Value Distribution Theory, Springer-Verlag & Science Press, Berlin, 1993.

[8] L. Zalcman, A heuristic principle in complex function theory, Amer. Math. Monthly 82(1975), 813—817.

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