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  • Cited by 8
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    WANG, YOU-MING 2015. The Normality of Meromorphic Functions with Multiple Zeros and Poles Concerning Sharing Values. Kyungpook mathematical journal, Vol. 55, Issue. 3, p. 641.

    Battaglia, Erika and Bonfiglioli, Andrea 2014. Normal families of functions for subelliptic operators and the theorems of Montel and Koebe. Journal of Mathematical Analysis and Applications, Vol. 409, Issue. 1, p. 1.

    LIAO, LIANG-WEN and YE, ZHUAN 2014. ON SOLUTIONS TO NONHOMOGENEOUS ALGEBRAIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATION. Journal of the Australian Mathematical Society, Vol. 97, Issue. 03, p. 391.

    Qi, Jianming Zhang, Guowei and Yuan, Wenjun 2014. Radically distributed value and normal families of meromorphic functions. Frontiers of Mathematics in China, Vol. 9, Issue. 2, p. 355.

    LEI, Chunlin FANG, Mingliang and ZENG, Cuiping 2013. Some Normality Criteria of Meromorphic Functions. Acta Mathematica Scientia, Vol. 33, Issue. 6, p. 1667.

    Chen, Wei Zhang, Yingying Zeng, Jiwen and Tian, Honggen 2012. Normal Criterion Concerning Shared Values. Journal of Applied Mathematics, Vol. 2012, p. 1.

    Chen, Jun-Fan 2012. A Note on the Growth of Meromorphic Functions with a Radially Distributed Value. Abstract and Applied Analysis, Vol. 2012, p. 1.

    Li, Yuntong 2012. Normal Families of Zero-Free Meromorphic Functions. Abstract and Applied Analysis, Vol. 2012, p. 1.

  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 139, Issue 5
  • October 2009, pp. 1091-1099

Picard values and normal families of meromorphic functions

  • Yan Xu (a1), Fengqin Wu (a1) and Liangwen Liao (a2)
  • DOI:
  • Published online: 01 September 2009

Let f be a transcendental meromorphic function on the complex plane ℂ, let a be a non-zero finite complex number and let n and k be two positive integers. In this paper, we prove that if nk+1, then assumes each value b∈ℂ infinitely often. Also, the related normal criterion for families of meromorphic functions is given. Our results generalize the related results of Fang and Zalcman.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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