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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
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 \[ |f(x + y) - f(x)f(y)| < \delta \] for some fixed $\delta$ and all x and y in the domain, then f is either bounded or exponential.


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Keywords: Functional equation, stability
Article copyright: © Copyright 1979 American Mathematical Society