Stability of the Cauchy functional equation in quasi-Banach spaces

Jacek Tabor. "Stability of the Cauchy functional equation in quasi-Banach spaces." Annales Polonici Mathematici 83.3 (2004): 243-255. <http://eudml.org/doc/280720>.

@article{JacekTabor2004,
abstract = {Let X be a quasi-Banach space. We prove that there exists K > 0 such that for every function w:ℝ → X satisfying ||w(s+t)-w(s)-w(t)|| ≤ ε(|s|+|t|) for s,t ∈ ℝ, there exists a unique additive function a:ℝ → X such that a(1)=0 and ||w(s)-a(s)-sθ(log₂|s|)|| ≤ Kε|s| for s ∈ ℝ, where θ: ℝ → X is defined by $θ(k):= w(2^k)/2^k$ for k ∈ ℤ and extended in a piecewise linear way over the rest of ℝ.},
author = {Jacek Tabor},
journal = {Annales Polonici Mathematici},
keywords = {stability; quasi-Banach space},
language = {eng},
number = {3},
pages = {243-255},
title = {Stability of the Cauchy functional equation in quasi-Banach spaces},
url = {http://eudml.org/doc/280720},
volume = {83},
year = {2004},
}

TY - JOUR
AU - Jacek Tabor
TI - Stability of the Cauchy functional equation in quasi-Banach spaces
JO - Annales Polonici Mathematici
PY - 2004
VL - 83
IS - 3
SP - 243
EP - 255
AB - Let X be a quasi-Banach space. We prove that there exists K > 0 such that for every function w:ℝ → X satisfying ||w(s+t)-w(s)-w(t)|| ≤ ε(|s|+|t|) for s,t ∈ ℝ, there exists a unique additive function a:ℝ → X such that a(1)=0 and ||w(s)-a(s)-sθ(log₂|s|)|| ≤ Kε|s| for s ∈ ℝ, where θ: ℝ → X is defined by $θ(k):= w(2^k)/2^k$ for k ∈ ℤ and extended in a piecewise linear way over the rest of ℝ.
LA - eng
KW - stability; quasi-Banach space
UR - http://eudml.org/doc/280720
ER -