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PDF(432 KB)
PDF(432 KB)
分担函数集的正规定则
Normal Criterion Concerning Shared Sets of Meromorphic Functions
本文将亚纯函数正规性与分担函数集相结合，探讨了亚纯函数族F正规与F中任意两个函数f与g分担函数的个数，f与其导数f'分担函数的个数及函数f的重值的个数三者之间的关系，给出了一个综合判定亚纯函数族正规的充分条件.
We study normality and shared sets of meromorphic functions. For a meromorphic family F, we investigate the relations among numbers of any two functions f, g shared functions, f and its derivative shared functions and multiple values of f. We give a quite general sufficient condition for F to be normal.
亚纯函数 / 正规族 / 分担函数 / 分担集合 {{custom_keyword}} /
meromorphic functions / normal families / shared functions / shared sets {{custom_keyword}} /
[1] Fang M. L., Hong W., Some results on normal of meromorphic function, Bull. Malays. Math. Sci. Soc., 2000, 23(2):143-151.
[2] Fang M. L., Zalcman L., A note on normality and shared values, J. Aust. Math. Soc., 2004, 76:141-150.
[3] Fang M. L., Zalcman L., Normal families and shared values of meromorphic function Ⅲ, Comput. Methods. Funct. Theory, 2002, 2(2):385-395.
[4] Gu Y. X., Pang X. C., Fang M. L., The Theory of Normal Family and Its Application (in Chinese), Science Press, Beijing, 2007.
[5] Hayman W. K., Meromorphic Functions, Clarendon Press, Oxford, 1964.
[6] Liu X. J., Pang X. C., Shared values and normal families, Acta Math. Sin., Chin. Ser., 2007, 50(2):409-412.
[7] Miranda R., Algebraric Curves and Riemann Surfaces (Graduate Studies in Mathematics Vol. 5), Amer. Math. Soc. Press, American, 1995.
[8] Pang X. C., Zalcman L., Normal families and shared values, Bull. London Math. Soc., 2000, 32:325-331.
[9] Pang X. C., Zalcman L., Normality and shared values, Ark. Math., 2000, 38:171-182.
[10] Qiu H. L., Fang C. Y., Fang M. L., Normal families concerning exceptional functions and shared functions, Acta Math. Sin., Chin. Ser., 2015, 58(2):345-352.
[11] Schweizer A., A normality criterion corresponding to the defect relations, Comput. Methods Funct. Theory, 2017, 17:591-601.
[12] Schwick W., Shared values and normality, Arch Math., 1992, 59:50-54.
[13] Yang L., Value Distribution Theory, Springer-Verlag, Berlin, 1993.
[14] Zalcman L., Normal families:New perspectives, Bull. Amer. Math. Soc., 1998, 35:215-230.
[15] Zhang Q., Normal criteria concerning sharing values, Kodai Math. J., 2002, 25:8-14.
国家自然科学基金资助项目（11371149）；广东省教育厅科研项目（2017KTSCX130）；广东金融学院科研项目（15XJ01-03，20170502152）
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