aequationes mathematicae

, Volume 54, Issue 1–2, pp 74–86 | Cite as

On Hyers-Ulam stability for a class of functional equations

  • Costanza Borelli
Research Papers


In this paper we prove some stability theorems for functional equations of the formg[F(x, y)]=H[g(x), g(y), x, y]. As special cases we obtain well known results for Cauchy and Jensen equations and for functional equations in a single variable.

AMS (1991) subject classification

39B52 39B72 47H15 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Aczél, J.,Lectures on functional equations and their applications. Academic Press, New York-London, 1966.zbMATHGoogle Scholar
  2. [2]
    Baker, J. A.,The stability of certain functional equations. Proc. Amer. Math. Soc.112 (1991), 729–732.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Borelli, C. andForti, G. L.,On a general Hyers-Ulam stability result. Internat. J. Math. Math. Sci.18 (1995), 229–236.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Forti, G. L.,An existence and stability theorem for a class of functional equations. Stochastica4 (1980), 23–30.zbMATHMathSciNetGoogle Scholar
  5. [5]
    Johnson, B. E.,Approximately multiplicative maps between Banach algebras. J. London Math. Soc. (2)37 (1988), 294–316.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Kuczma, M.,Functional equations in a single variable, Monografie Mat. 46, Polish Scientific Publishers (PWN), Warszawa, 1968.zbMATHGoogle Scholar

Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  • Costanza Borelli
    • 1
  1. 1.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly

Personalised recommendations