Uniqueness of entire functions and fixed points

• Autorzy: Xiao-Guang Qi , Lian-Zhong Yang
• Języki publikacji: EN

Abstrakty

EN

Let f and g be entire functions, n, k and m be positive integers, and λ, μ be complex numbers with |λ| + |μ| ≠ 0. We prove that $(fⁿ(z)(λf^m(z)+μ))^(k)$ must have infinitely many fixed points if n ≥ k + 2; furthermore, if $(fⁿ(z)(λf^m(z)+μ))^(k)$ and $(gⁿ(z)(λg^m(z)+μ))^(k)$ have the same fixed points with the same multiplicities, then either f ≡ cg for a constant c, or f and g assume certain forms provided that n > 2k + m* + 4, where m* is an integer that depends only on λ.

Kategorie tematyczne

• 30D20: Entire functions, general theory
• 30D35: Distribution of values, Nevanlinna theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2010
• Tom: 97
• Numer: 1
• Strony: 87-100

Daty

wydano

2010

Twórcy

autor

Xiao-Guang Qi

• School of Mathematics, Shandong University, Jinan, Shandong, 250100, P.R. China

autor

Lian-Zhong Yang

• School of Mathematics, Shandong University, Jinan, Shandong, 250100, P.R. China

Identyfikatory

DOI

10.4064/ap97-1-7