Generalized stability of isometries in p-homogeneous F-spaces

• Autorzy: Żołdak M.
• Języki publikacji: EN

Abstrakty

EN

Let X, Y be p-homogeneous, complete F-spaces, r > 0, δ > 0. A function ƒ: X→Y is an (r, δ)-isometry, if (…) for x, y ∈ X. We consider the following problem: does for each ε > 0, r > 0 there exist a δ > 0 such that for each surjective (r, δ)-isometry ƒ there exists an isometry U : X → Y such that (…).

Słowa kluczowe

EN

δ-isometry; stability of isometries

PL

δ-izometria; stabilność izometrii

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2011
• Tom: Vol. 44, nr 2
• Strony: 335--348
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Żołdak M.

• Department of Mathematics, University of Rzeszów, Rejtana 16a, Rzeszów 35-310, Poland

Bibliografia

• [1] Y.Benyamini, J.Lindenstrauss, Geometric Nonlinear Functional Analysis I Amer. Math.Soc. Colloquium Publications,Vol.48, Amer.Math.Soc., Providence, RI, 2000.
• [2] J.Gevirtz, Stability of isometries on Banach spaces Proc.Amer.Math.Soc. 89 (1983), 633–636.
• [3] D.H.Hyers, S.M.Ulam, On approximate isometries Bull.Amer.Math.Soc. 51 (1945), 288–292.
• [4] M.Omladič, P.Šemrl, On nonlinear perturbations of isometries Math.Ann. 303 (1995), 617–628.
• [5] S.Rolewicz, Metric Linear Spaces PWN, Warszawa 1972.
• [6] S.M.Ulam, A Collection of Mathematical Problems Interscience Publ., New York, 1960.
• [7] J.Tabor, J.Tabor, M.Żołdak, Stability of isometries in p-homogeneous F-spaces, Functiones et Approximatio 38.1 (2008), 109–119.