Stability of the Cauchy functional equation in quasi-Banach spaces

• Autorzy: Jacek Tabor
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46A16: Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
• 39B82: Stability, separation, extension, and related topics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2004
• Tom: 83
• Numer: 3
• Strony: 243-255

Daty

wydano

2004

Twórcy

autor

Jacek Tabor

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Identyfikatory

DOI

10.4064/ap83-3-6