Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T02:25:19.561Z Has data issue: false hasContentIssue false
  • English
  • Français

UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH WEAKLY WEIGHTED SHARING

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  28 June 2013

THAMIR ALZAHARY
THAMIR ALZAHARY*
Affiliation:
Korteweg-de Vries Institute for Mathematics, Amsterdam University, PO BOX 94248, Amsterdam 1090GE, The Netherlands email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we introduce the notion of weakly weighted sharing of zeros of meromorphic functions ignoring multiplicities, which extends the notion of weakly weighted sharing counting multiplicities, and we also introduce the notion of multiplicity. By using these notions, we prove some results on the uniqueness of meromorphic functions concerning differential polynomials sharing nonzero finite values. The results in this paper extend the results of Yang and Hua, Fang, and Dyavanal. In this paper, we correct defective points in the paper of Wu et al. [‘Uniqueness of meromorphic functions sharing one value’, Bull. Aust. Math. Soc. 85(2012), 280–294].

Keywords

meromorphic functiondifferential polynomialweakly weighted sharing

MSC classification

Secondary: 30D35: Distribution of values, Nevanlinna theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 1 , August 2013 , pp. 26 - 43
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Dyavanal, R. S., ‘Uniqueness and value-sharing of differential polynomials of meromorphic functions’, J. Math. Anal. Appl. 374 (2011), 335–345.CrossRefGoogle Scholar
Fang, M. L., ‘Uniqueness and value-sharing of entire functions’, Comput. Math. Appl. 44 (2002), 828–831.CrossRefGoogle Scholar
Hayman, W. K., Meromorphic Functions (Clarendon Press, Oxford, 1964).Google Scholar
Lin, S. H. and Lin, W. C., ‘Uniqueness of meromorphic functions concerning weakly weighted-sharing’, Kodai Math. J. 29 (2006), 269–280.CrossRefGoogle Scholar
Lin, W. C. and Yi, H. X., ‘Uniqueness theorems for meromorphic functions’, Indian J. Pure Appl. Math. 35 (2004), 121–132.Google Scholar
Wu, C., Mu, C. and Li, J., ‘Uniqueness of meromorphic functions sharing one value’, Bull. Aust. Math. Soc. 85 (2012), 280–294.CrossRefGoogle Scholar
Yang, C. C. and Hua, X. H., ‘Uniqueness and value-sharing of meromorphic functions’, Ann. Acad. Sci. Fenn. Math. 22 (1997), 395–406.Google Scholar
Yang, C. C. and Yi, H. X., Uniqueness Theory of Meromorphic Functions (Kluwer Academic Publishers, Dordrecht, 2003).CrossRefGoogle Scholar