Abstract
In this paper, we proved some normality criteria for a family of meromorphic functions, where a holomorphic function is shared by every function from the family and a linear differential polynomial generated by the members of the family.
Similar content being viewed by others
References
L. V. Ahlfors, Complex analysis, Third edition, McGraw-Hill, 1979.
W. Bergweiler and A. Eremenko, On the singularities of the inverse to a meromorphic function of finite order, Rev. Mat. Iberoamericana, 11(2) (1995), 355–5.
H. H. Chen and M. L. Fang, Shared values and normal families of meromorphic functions, J. Math. Anal. Appl., 260 (2001), 124–4.
J. F. Chen, Normal families and shared sets of meromorphic functions, Rocky Mountain J. Math., 41(1) (2011), 37–5.
J. F. Chen and M. L. Fang, Normal families and shared functions of meromorphic functions, Israel J. Math., 180 (2010), 129–4.
M. L. Fang, Picard values and normality criterion, Bull. Korean Math. Soc., 38(2) (2001), 379–5.
M. L. Fang and Y. Xu, Normal families of holomorphic functions and shared values, Israel J. Math., 129 (2002), 125–4.
M. Han and Y. Gu, The normal family of meromophic functions, Acta Math. Sci., 28B(4) (2008), 759–762.
W. K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964.
E. Mues and N. Steinmentz, Meromorphe functionen, die mit ihrer ableitung werte teilen, Manuscripta Mathematica, 29 (1979), 195–4.
X. Pang and L. Zalcman, Normality and shared values, Ark. Mat., 38 (2000), 171–4.
J. Schiff, Normal families, Springer-Verlag, Berlin, 1993.
W. Schwick, Sharing values and normality, Archiv der Mathematik, 59 (1992), 50–4.
Y. F. Wang and M. L. Fang, Picard values and normal families of meromorphic functions with multiple zeros, Acta Math. Sin., new series, 14(1) (1998), 17–5.
J. Xia and Y. Xu, Normality criterion concerning sharing functions II, Bull. Malays. Math. Sci. Soc. (2), 33(3) (2010), 479–5.
Y. Xu, Normality criterion concerning sharing functions, Houstan J. Math., 32(3) (2006), 945–5.
C. C. Yang and H. X. Yi, Uniqueness theory of meromorphic functions, Science Press/Kluwer Academic Publishers, 2003.
L. Yang, Value distribution theory, Springer-Verlag, Berlin, 1993.
L. Zalcman, A heuristic principle in complex function theory, The Amer. Math. Monthly, 82 (1975), 813–4.
L. Zalcman, Normal families: new perspective, Bull. of Amer. Math. Soc., 35 (1998), 215–4.
Author information
Authors and Affiliations
Corresponding author
Additional information
The research work of the first author is supported by junior research fellowship from UGC India.
Rights and permissions
About this article
Cite this article
Datt, G., Kumar, S. Normality and sharing functions. Indian J Pure Appl Math 46, 853–864 (2015). https://doi.org/10.1007/s13226-015-0155-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13226-015-0155-2