Uniqueness of entire functions and fixed points

Xiao-Guang Qi, and Lian-Zhong Yang. "Uniqueness of entire functions and fixed points." Annales Polonici Mathematici 97.1 (2010): 87-100. <http://eudml.org/doc/280331>.

@article{Xiao2010,
abstract = {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.},
author = {Xiao-Guang Qi, Lian-Zhong Yang},
journal = {Annales Polonici Mathematici},
keywords = {entire functions; meromorphic functions; sharing values; differential polynomial},
language = {eng},
number = {1},
pages = {87-100},
title = {Uniqueness of entire functions and fixed points},
url = {http://eudml.org/doc/280331},
volume = {97},
year = {2010},
}

TY - JOUR
AU - Xiao-Guang Qi
AU - Lian-Zhong Yang
TI - Uniqueness of entire functions and fixed points
JO - Annales Polonici Mathematici
PY - 2010
VL - 97
IS - 1
SP - 87
EP - 100
AB - 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.
LA - eng
KW - entire functions; meromorphic functions; sharing values; differential polynomial
UR - http://eudml.org/doc/280331
ER -