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aequationes mathematicae

, Volume 64, Issue 1–2, pp 62–69 | Cite as

On the Hyers-Ulam stability problem for quadratic multi-dimensional mappings

  • J. M. Rassias
Article

Summary.

In 1940 S. M. Ulam proposed the well-known Ulam stability problem. In 1941 D. H. Hyers solved this problem for linear mappings. According to P. M. Gruber (1978) this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types. In 1982-1999 we solved the above Ulam problem for different mappings. In this paper we solve the Hyers-Ulam stability problem for quadratic multi-dimensional mappings.

Keywords. General stability problem, Hyers-Ulam stability, square of the quadratic weighted mean, quadratic mapping. 

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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • J. M. Rassias
    • 1
  1. 1.Pedagogical Department, E.E., National and Capodistrian University of Athens, 4, Agamemnonos Str., Aghia Paraskevi, Athens 15342, Greece,¶ e-mail: jrassias@primetu.uoa.grGR

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