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NORMAL FAMILIES OF ZERO-FREE MEROMORPHIC FUNCTIONS

Published online by Cambridge University Press:  16 November 2011

BINGMAO DENG
Affiliation:
Institute of Applied Mathematics, South China Agricultural University, Guangzhou 510642, PR China (email: [email protected])
MINGLIANG FANG*
Affiliation:
Institute of Applied Mathematics, South China Agricultural University, Guangzhou 510642, PR China (email: [email protected])
DAN LIU
Affiliation:
Institute of Applied Mathematics, South China Agricultural University, Guangzhou 510642, PR China (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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Let ℱ be a family of zero-free meromorphic functions in a domain D, let h be a holomorphic function in D, and let k be a positive integer. If the function f(k)h has at most k distinct zeros (ignoring multiplicity) in D for each f∈ℱ, then ℱ is normal in D.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

Research supported by the NNSF of China (Grant No. 11071083).

References

[1]Chang, J. M., ‘Normality and quasinormality of zero-free meromorphic functions’, Acta Math. Sin. (Engl. Ser.), to appear.Google Scholar
[2]Gu, Y. X., ‘A criterion for normality of families of meromorphic functions’, Sci. Sin. 1 (1979), 267274.Google Scholar
[3]Hayman, W. K., ‘Picard values of meromorphic functions and their derivatives’, Ann. of Math. (2) 70 (1959), 942.CrossRefGoogle Scholar
[4]Hayman, W. K., Meromorphic Functions (Clarendon Press, Oxford, 1964).Google Scholar
[5]Hayman, W. K., Research Problems in Function Theory (Athlone Press, London, 1967).Google Scholar
[6]Mirsky, L., An Introduction to Linear Algebra (Clarendon Press, Oxford, 1955).Google Scholar
[7]Pang, X. C., Yang, D. G. and Zalcman, L., ‘Normal families of meromorphic functions whose derivatives omit a function’, Comput. Methods Funct. Theory 2 (2002), 257265.CrossRefGoogle Scholar
[8]Pang, X. C. and Zalcman, L., ‘Normal families and shared values’, Bull. Lond. Math. Soc. 32 (2000), 325331.CrossRefGoogle Scholar
[9]Schiff, J., Normal Families (Springer, Berlin–Heidelberg–New York, 1993).CrossRefGoogle Scholar
[10]Yang, L., ‘Normality for families of meromorphic functions’, Sci. Sin. 29 (1986), 12631274.Google Scholar
[11]Yang, L., Value Distribution Theory (Springer, Berlin–Heidelberg–New York, 1993).Google Scholar
[12]Zalcman, L., ‘Normal families: new perspectives’, Bull. Amer. Math. Soc. 35 (1998), 215230.CrossRefGoogle Scholar