Normal families and shared values of meromorphic functions

• Autorzy: Mingliang Fang , Lawrence Zalcman
• Języki publikacji: EN

Abstrakty

EN

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,....

Kategorie tematyczne

• 30D45: Bloch functions, normal functions, normal families

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2003
• Tom: 80
• Numer: 1
• Strony: 133-141

Daty

wydano

2003

Twórcy

autor

Mingliang Fang

• Department of Mathematics, Nanjing Normal University, Nanjing 210097, P.R. China

autor

Lawrence Zalcman

• Department of Mathematics and Statistics, Bar-Ilan University, 52900 Ramat-Gan, Israel

Identyfikatory

DOI

10.4064/ap80-0-11