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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

Functional Equation Banach Algebra Multiplicative Mapping Compact Abelian Group Jordan Block 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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