Abstract
In this article, we prove a normality criterion for a family of meromorphic functions having zeros with some multiplicity which involves sharing of a holomorphic function by the members of the family. Our result generalizes Montel’s normality test in a certain sense.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. V. Ahlfors, Complex Analysis. An introduction to the theory of analytic functions of one complex variable, Third edition, International Series in Pure and Applied Mathematics, McGraw-Hill Book Co., New York, 1978.
Datt G., Kumar S.: Normality and sharing functions. Indian J. Pure Appl. Math. 46, 853–864 (2015)
G. Datt and S. Kumar, Some normality criteria, Turkish J. Math. (accepted for publication), arXiv:1403.1447[math.CV].
Hayman W. K.: Meromorphic Functions. Clarendon Press, Oxford (1964)
Schiff J.: Normal Families. Springer-Verlag, Berlin (1993)
Schwick W.: Sharing values and normality. Arch. Math. 59, 50–54 (1992)
Sun D. C.: The shared value criterion for normality. J. Wuhan Univ. Natur. Sci. Ed. 3, 9–12 (1994)
Xu Y.: On Montel’s theorem and Yang’s problem. J. Math. Anal. Appl. 305, 743–751 (2005)
Xu Y.: Montel’s criterion and shared function. Publ. Math. Debrecen 77, 471–478 (2010)
Yang L.: Value Distribution Theory. Springer-Verlag, Berlin (1993)
Zalcman L.: Normal families: new perspectives. Bull. Amer. Math. Soc. 35, 215–230 (1998)
Author information
Authors and Affiliations
Corresponding author
Additional information
The research work of Gopal Datt is supported by research fellowship from UGC India.
Rights and permissions
About this article
Cite this article
Datt, G., Kumar, S. Normality and Montel’s Theorem. Arch. Math. 107, 511–521 (2016). https://doi.org/10.1007/s00013-016-0954-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-016-0954-7