Normal families and shared values of meromorphic functions
Mingliang Fang ; Lawrence Zalcman
Annales Polonici Mathematici, Tome 81 (2003), p. 133-141 / Harvested from The Polish Digital Mathematics Library
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Let ℱ be a family of meromorphic functions on a plane domain D, all of whose zeros are of multiplicity at least k ≥ 2. Let a, b, c, and d be complex numbers such that d ≠ b,0 and c ≠ a. If, for each f ∈ ℱ, f(z)=a⇔f(k)(z)=b, and f(k)(z)=d⇒f(z)=c, then ℱ is a normal family on D. The same result holds for k=1 so long as b≠(m+1)d, m=1,2,....

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:280651 
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Mingliang Fang; Lawrence Zalcman. Normal families and shared values of meromorphic functions. Annales Polonici Mathematici, Tome 81 (2003) pp. 133-141. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap80-0-11/