Fixed points of meromorphic functions and of their differences and shifts

Zong-Xuan Chen. "Fixed points of meromorphic functions and of their differences and shifts." Annales Polonici Mathematici 109.2 (2013): 153-163. <http://eudml.org/doc/280184>.

@article{Zong2013,
abstract = {Let f(z) be a finite order transcendental meromorphic function such that λ(1/f(z)) < σ(f(z)), and let c ∈ ℂ∖0 be a constant such that f(z+c) ≢ f(z) + c. We mainly prove that $max\{τ(f(z)),τ(Δ_\{c\}f(z))\} = max\{τ(f(z)),τ(f(z+c))\} = max\{τ(Δ_\{c\}f(z)),τ(f(z+c))\} = σ(f(z))$, where τ(g(z)) denotes the exponent of convergence of fixed points of the meromorphic function g(z), and σ(g(z)) denotes the order of growth of g(z).},
author = {Zong-Xuan Chen},
journal = {Annales Polonici Mathematici},
keywords = {meromorphic function; complex difference; shift; fixed point},
language = {eng},
number = {2},
pages = {153-163},
title = {Fixed points of meromorphic functions and of their differences and shifts},
url = {http://eudml.org/doc/280184},
volume = {109},
year = {2013},
}

TY - JOUR
AU - Zong-Xuan Chen
TI - Fixed points of meromorphic functions and of their differences and shifts
JO - Annales Polonici Mathematici
PY - 2013
VL - 109
IS - 2
SP - 153
EP - 163
AB - Let f(z) be a finite order transcendental meromorphic function such that λ(1/f(z)) < σ(f(z)), and let c ∈ ℂ∖0 be a constant such that f(z+c) ≢ f(z) + c. We mainly prove that $max{τ(f(z)),τ(Δ_{c}f(z))} = max{τ(f(z)),τ(f(z+c))} = max{τ(Δ_{c}f(z)),τ(f(z+c))} = σ(f(z))$, where τ(g(z)) denotes the exponent of convergence of fixed points of the meromorphic function g(z), and σ(g(z)) denotes the order of growth of g(z).
LA - eng
KW - meromorphic function; complex difference; shift; fixed point
UR - http://eudml.org/doc/280184
ER -