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

Baker, John; Lawrence, J.; Zorzitto, F.

doi:10.1090/S0002-9939-1979-0524294-6

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The stability of the equation $f(x+y)=f(x)f(y)$
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by John Baker, J. Lawrence and F. Zorzitto PDF

Proc. Amer. Math. Soc. 74 (1979), 242-246 Request permission

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.

References

D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222–224. MR 4076, DOI 10.1073/pnas.27.4.222