Abstract and Applied Analysis

Normal Families of Zero-Free Meromorphic Functions

Yuntong Li

Full-text: Open access


Let a ( 0 ) , b , and n and k be two positive integers such that n 2 . Let be a family of zero-free meromorphic functions defined in a domain 𝒟 such that for each f , f + a ( f ( k ) ) n b has at most n k zeros, ignoring multiplicity. Then is normal in 𝒟 .

Article information

Abstr. Appl. Anal., Volume 2012 (2012), Article ID 908123, 12 pages.

First available in Project Euclid: 14 December 2012

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Li, Yuntong. Normal Families of Zero-Free Meromorphic Functions. Abstr. Appl. Anal. 2012 (2012), Article ID 908123, 12 pages. doi:10.1155/2012/908123. https://projecteuclid.org/euclid.aaa/1355495834

Export citation


  • J. L. Schiff, Normal Families, Springer, Berlin, Germany, 1993.
  • W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, UK, 1964.
  • C.-C. Yang and H.-X. Yi, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, China, 1995.
  • C.-C. Yang and H.-X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic, Dordrecht, The Netherland, 2003.
  • W. K. Hayman, “Picard values of meromorphic functions and their derivatives,” Annals of Mathematics. Second Series, vol. 70, pp. 9–42, 1959.
  • E. Mues, “Über ein Problem von Hayman,” Mathematische Zeitschrift, vol. 164, no. 3, pp. 239–259, 1979.
  • Y. S. Ye, “A Picard type theorem and Bloch law,” Chinese Annals of Mathematics B, vol. 15, no. 1, pp. 75–80, 1994.
  • M. L. Fang and L. Zalcman, “On value distribution of $f+a{({f}^{\prime })}^{n}$,” Science A, vol. 38, pp. 279–285, 2008.
  • Y. Xu, F. Wu, and L. Liao, “Picard values and normal families of meromorphic functions,” Proceedings of the Royal Society of Edinburgh A, vol. 139, no. 5, pp. 1091–1099, 2009.
  • J. M. Chang, “Normality and quasinormality of zero-free meromorphic functions,” Acta Mathematica Sinica, vol. 28, no. 4, pp. 707–716, 2012.
  • L. Mirsky, An Introduction to Linear Algebra, Clarendon Press, Oxford, UK, 1955.
  • X. Pang and L. Zalcman, “Normal families and shared values,” The Bulletin of the London Mathematical Society, vol. 32, no. 3, pp. 325–331, 2000.