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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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
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.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0524294-6
PII: S 0002-9939(1979)0524294-6
Keywords: Functional equation, stability
Article copyright: © Copyright 1979 American Mathematical Society