Aequationes mathematicae

, Volume 90, Issue 6, pp 1195–1200 | Cite as

A note on stability of maps which preserve equality of distance

  • Yunbai Dong


In this note, we show a generalized stability of maps which preserve equality of distance.


Stability Banach spaces Isometries 

Mathematics Subject Classification

Primary 39B82 Secondary 46B04 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Badora R.: On Hyers–Ulam stability of Wilson’s functional equation. Aequ. Math. 60, 211–218 (2000)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Brzdȩk J.: Stability of the equation of the p-Wright affine functions. Aequ. Math. 85, 497–503 (2013)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Brzdȩk J., Popa D., Xu B.: Hyers–Ulam stability for linear equations of higher orders. Acta Math. Hung. 120, 1–8 (2008)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Dong Y.: On approximate isometries and application to stability of a functional equation. J. Math. Anal. Appl. 426, 125–137 (2015)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Dong Y., Zheng B.: On hyperstability of additive mappings onto Banach spaces. Bull. Aust. Math. Soc. 91, 278–285 (2015)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Hyers D.H.: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. 27, 222–224 (1941)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Jung S.M.: Hyers–Ulam–Rassias Stability of Functional Equations in Nonlinear Analysis. Springer Optimization and Its Applications, vol. 48. Springer, New York (2011)Google Scholar
  8. 8.
    Jung S.M., Popa D., Rassias M.Th.: On the stability of the linear functional equation in a single variable on complete metric groups. J. Glob. Optim. 59, 165–171 (2014)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Piszczek M.: The properties of functional inclusions and Hyers–Ulam stability. Aeq. Math. 85, 111–118 (2013)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Rassias J.M.: On the Hyers–Ulam stability problem for quadratic multi-dimensional mappings. Aequ. Math. 64, 62–69 (2002)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Rassias T.M.: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72, 297–300 (1978)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Rassias T.M.: On the stability of functional equations in Banach space. J. Math. Anal. Appl. 251, 264–284 (2000)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Sikorska J.: Stability of the preservation of the equality of distance. J. Math. Anal. Appl. 311, 209–217 (2005)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Tabor J.: Stability of the Fischer-Muszély functional equation. Publ. Math. Debr. 62, 205–211 (2003)MathSciNetMATHGoogle Scholar
  15. 15.
    Ulam S.M.: A Collection of Mathematical Problems, pp. 63. Interscience Publishers, New York (1968)Google Scholar
  16. 16.
    Vogt A.: Maps which preserve equality of distance. Stud. Math. 45, 43–48 (1973)MathSciNetMATHGoogle Scholar

Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.School of Mathematics and ComputerWuhan Textile UniversityWuhanChina

Personalised recommendations