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The stability of the equation $ f(x+y)=f(x)f(y)$


Authors: John Baker, J. Lawrence and F. Zorzitto
Journal: Proc. Amer. Math. Soc. 74 (1979), 242-246
MSC: Primary 39B50
DOI: https://doi.org/10.1090/S0002-9939-1979-0524294-6
MathSciNet review: 524294
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Abstract: It is proved that if f is a function from a vector space to the real numbers satisfying

$\displaystyle \vert f(x + y) - f(x)f(y)\vert < \delta $

for some fixed $ \delta $ and all x and y in the domain, then f is either bounded or exponential.

References [Enhancements On Off] (What's this?)

  • [1] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222–224. MR 0004076

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0524294-6
Keywords: Functional equation, stability
Article copyright: © Copyright 1979 American Mathematical Society