Uniqueness of entire functions and fixed points
Xiao-Guang Qi ; Lian-Zhong Yang
Annales Polonici Mathematici, Tome 98 (2010), p. 87-100 / Harvested from The Polish Digital Mathematics Library
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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)(λfm(z)+μ))(k) must have infinitely many fixed points if n ≥ k + 2; furthermore, if (fⁿ(z)(λfm(z)+μ))(k) and (gⁿ(z)(λgm(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.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:280331 
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Xiao-Guang Qi; Lian-Zhong Yang. Uniqueness of entire functions and fixed points. Annales Polonici Mathematici, Tome 98 (2010) pp. 87-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap97-1-7/