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Meromorphic Functions That Share One Finite Value CM or IM with Their First Derivative | ||
| Journal of University of Anbar for Pure Science | ||
| Article 21, Volume 3, Issue 3, 2009, Pages 69-73 PDF (333.45 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.37652/juaps.2009.15579 | ||
| Author | ||
| Amer H. H. Al-Khaladi* | ||
| Diyala University - College of Science | ||
| Abstract | ||
| In this paper we shall prove that if a non-constant meromorphic function and its derivative share the value CM (IM) and if ( ), then either or ( ), where and are constants. These results give improvement and extension of the following result of Gundersen: if a non-constant meromorphic function and its derivative share two distinct values CM, then . | ||
| Keywords | ||
| Nevanlinna theory; uniqueness theorem; share CM or IM; Classification Categories; Subject classification | ||
| References | ||
|
[1] W. K. Hayman (1964). Meromorphic functions, Clarendon Press, Oxford.
[2] R. Nevanlinna (1929). Le théorème de Picard-Borel et la théorie des functions méromorphes, Gauthiers-Villars, Paris.
[3] G. G. Gundersen (1980). Meromorphic functions that share finite values with their derivative. J. Math. Anal. Appl., 75: 441-446. | ||
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