Approximately Multiplicative Mappings. Superstability

  • Donald H. Hyers
  • George Isac
  • Themistocles M. Rassias
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 34)

Abstract

The stability of the functional equation f (x + y) = f (x) f (y) was studied by J. Baker, J. Lawrence and F. Zorzitto (1979). They proved that if f is a function from a real vector space W to the real numbers satisfying |f (x+y) -f (x) f (y) | < δ for some fixed δ> 0 and all x, y in W, then f is either bounded or else f (x + y) = f (x)f (y) for all x,y in W.

Keywords

Convolution 

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Donald H. Hyers
  • George Isac
    • 1
  • Themistocles M. Rassias
    • 2
  1. 1.Department of Mathematics and Computer ScienceRoyal Military College of CanadaKingstonCanada
  2. 2.Department of MathematicsNational Technical University of AthensAthensGreece

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