Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Further Results about the Normal Family of Meromorphic Functions and Shared Sets

  • Qi, Jianming (Department of Mathematics and Physics, Shanghai Dianji University) ;
  • Zhang, Guowei (School of Mathematics and Statistics, Anyang Normal University) ;
  • Zhou, Linlin (Department of Mathematics, Zhenjiang watercraft college)
  • Received : 2010.03.03
  • Accepted : 2011.09.23
  • Published : 2012.03.23
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Abstract

Let $\mathcal{F}$ be a family of meromorphic functions in a domain D, and let $k$, $n({\geq}2)$ be two positive integers, and let $S=\{a_1,a_2,{\ldots},a_n\}$, where $a_1$, $a_2$, ${\ldots}$, $a_n$ are distinct finite complex numbers. If for each $f{\in}\mathcal{F}$, all zeros of $f$ have multiplicity at least $k+1$, $f$ and $G(f)$ share the set $S$ in $D$, where $G(f)=P(f^{(k)})+H(f)$ is a differential polynomial of $f$, then$\mathcal{F}$ is normal in $D$.

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References

  1. W. Bergweiler and A. Eremenko, On the singularities of the inverse to a meromorphic function of finite order, Rev. Mat. Iber., 11(1995), 355-373.
  2. M. L. Fang and L. Zalcman, Normal families and shared values of meromorphic functions III, Comput. Methods Funct. Theory, 2(2002), 385-395.
  3. W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
  4. C. L. Lei, M. L. Fang and D. G. Yang, Normal of meromorphic functions and shared sets, Advance in Inequalities for Series., (2008), 155-162.
  5. X. C. Pang and L. Zalcman, Normality and shared values, Ark. Mat., 38(2000), 171- 182. https://doi.org/10.1007/BF02384496
  6. X. C. Pang and L. Zalcman, Normal families and shared values, Bull. London Math. Soc., 32 (2000), 325-331. https://doi.org/10.1112/S002460939900644X
  7. W. Schwick, Sharing values and normality, Arch Math., 59(1992), 50-54. https://doi.org/10.1007/BF01199014
  8. Y. F. Wang and M. L. Fang, Picard values and normal families of meromorphic functions with zeros, Acta Math., Sinica, New Series, 14(1)(1998), 17-26. https://doi.org/10.1007/BF02563879
  9. L. Zalcman, Normal families new perspectives, Bull. Amer. Math. Soc., 35(1998), 215-230. https://doi.org/10.1090/S0273-0979-98-00755-1