Aequationes mathematicae

, Volume 87, Issue 1–2, pp 165–171 | Cite as

On Tabor groupoids and stability of some functional equations

  • Roman Badora
  • Barbara Przebieracz
  • Peter Volkmann
Open Access


Two results are given, which use Tabor groupoids for questions of stability in the sense of Pólya–Szegő–Hyers–Ulam. We also start to study Tabor groupoids in their own right.

Mathematics Subject Classification (2010)

20N02 39B82 


Tabor groupoids stability of functional equations bounded perturbations of additive functions 


  1. 1.
    Badora, R., Przebieracz, B., Volkmann, P.: Stability of the Pexider functional equation. Ann. Math. Silesianae 24(2010), 7–13 (2011)Google Scholar
  2. 2.
    Badora, R., Przebieracz, B., Volkmann, P.: Stability of the functional equation f(xy) = f(yx) on groups, Remark at the Eleventh Katowice-Debrecen Winter Seminar on Functional Equations and Inequalities, Wisła-Malinka 2011. Ann. Math. Silesianae 25(2011), 116 (2012)Google Scholar
  3. 3.
    Ger R., Volkmann P.: On sums of linear and bounded mappings. Abh. Math. Sem. Univ. Hamburg 68, 103–108 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Gilányi, A., Nagatou, K., Volkmann, P.: Stability of a functional equation coming from the characterization of the absolute value of additive functions. Ann. Funct. Anal. 1(2), 1–6 (2011).
  5. 5.
    Golovina L.I.: Linejnaâ algebra i nekotorye ee priloženiâ. Nauka, Moskva (1971)Google Scholar
  6. 6.
    Griffin H.: Elementary theory of numbers. McGraw-Hill, New York (1954)zbMATHGoogle Scholar
  7. 7.
    Ma, H., Volkmann, P.: On bounded perturbations of linear operators. EVA STAR (2012), 5 pp.
  8. 8.
    Simon (Chaljub-Simon) A., Volkmann P.: Caractérisation du module d’une fonction additive à l’aide d’une équation fonctionnelle. Aequationes Math. 47, 60–68 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Tabor, J.: Remark 18, 22nd International Symposium on Functional Equations, Oberwolfach 1984. Aequationes Math. 29, 96 (1985)Google Scholar
  10. 10.
    Volkmann, P.: On the stability of the Cauchy equation. In: Proceedings of the Numbers, Functions, Equations ’98 International Conference, edited by Zsolt Páles, Janus Pannonius Tudományegyetem Pécs, pp. 150–151 (1998)Google Scholar
  11. 11.
    Volkmann, P.: O stabilności równań funkcyjnych o jednej zmiennej. Sem. LV No. 11 (2001), 6 pp., Errata ibid. No. 11bis (2003), 1 p.

Copyright information

© The Author(s) 2013

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  • Roman Badora
    • 1
  • Barbara Przebieracz
    • 1
  • Peter Volkmann
    • 1
    • 2
  1. 1.Instytut MatematykiUniwersytet Śla̧skiKatowicePoland
  2. 2.Institut für AnalysisKITKarlsruheGermany

Personalised recommendations