Rocky Mountain Journal of Mathematics

Normality concerning exceptional functions

Chunnuan Cheng and Yan Xu

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Let $\varphi(z)(\not\equiv0)$ be a function holomorphic in a domain $D$, $k\in\mathbb{N}$, and let $\mathcal{F}$ be a family of meromorphic functions defined in $D$, all of whose zeros have multiplicity at least $k+2$ such that, for every $f\in\mathcal{F}$, $f^{(k)}(z)\neq\varphi(z)$. The non-normal sequences in $\mathcal{F}$ are characterized.

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Rocky Mountain J. Math., Volume 45, Number 1 (2015), 157-168.

First available in Project Euclid: 7 April 2015

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Meromorphic functions normal family exception function


Cheng, Chunnuan; Xu, Yan. Normality concerning exceptional functions. Rocky Mountain J. Math. 45 (2015), no. 1, 157--168. doi:10.1216/RMJ-2015-45-1-157.

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  • J.M. Chang, Normal families of meromorphic functions whose derivatives omit a holomorphic function, Science in China, Series: Maththatics, to appear.
  • M.L. Fang, Picard values and normality criterion, Bull. Korean Math. Soc. 38 (2001), 379–387.
  • Y.X. Gu, A normal criterion of meromorphic families, Scientia, Math. Issue I (1979), 276–274.
  • W.K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964.
  • ––––, Research problems in function theory, Athlone Press, London, 1967.
  • X.C. Pang, M.L. Fang and L. Zalcman, Normal families of holomorphic functions with multiple zeros, Conf. Geom. Dyn. 11 (2007), 101–106.
  • X.C. Pang, D.G. Yang and L. Zalcman, Normal families of meromorphic functions whose derivatives omit a function, Comp. Meth. Funct. 2 (2002), 257–265.
  • X.C. Pang and L. Zalcman, Normal families and shared values, Bull. Lond. Math. Soc. 32 (2000), 325–331.
  • ––––, Normal families of meromorphic functions with multiple zeros and poles, Israel J. Math. 136 (2003), 1–9.
  • J. Schiff, Normal families, Springer-Verlag, New York,1993.
  • Y.F. Wang and M.L. Fang, Picard values and normal families of meromorphic functions with multiple zeros, Acta Math. Sinica 14 (1998), 17–26.
  • Y. Xu, Normality and exceptional functions of derivatives, J. Aust. Math. Soc. 76 (2004), 403–413.
  • L. Yang, Value distribution theory, Springer-Verlag & Science Press, Berlin, 1993.