HOME > Table of Contents and Abstracts > Vol. 63, No. 2
Tohoku Mathematical Journal
SECOND SERIES VOL. 63, NO. 2
|Tohoku Math. J.|
63 (2011), 149-162
SHARED VALUES, PICARD VALUES AND NORMALITY
Jianming Chan and Yuefei Wang
(Received November 27, 2009, revised July 12, 2010)
It is known that a family of meromorphic functions is normal if each function in the family shares a 3-element set with its derivative. In this paper we consider value distribution and normality problems with regard to 2-element shared sets. First we construct an example, by use of the Weierstrass doubly periodic functions, to show that a 3-element shared set can not be reduced to a 2-element shared set in general. We obtain a new criterion of normal families and new Picard-type theorems. The proofs make use of some results in complex dynamics. More examples are constructed to show that our assumptions are necessary.
2000 Mathematics Subject Classification.
Primary 30D45; Secondary 30D35.
Key words and phrases.
Meromorphic functions, normality, shared values and sets.
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