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

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ISSN 1088-6826(online) ISSN 0002-9939(print)

The stability of the equation

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.

[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 (2,315a)

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