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
Additional Information
- © Copyright 1979 American Mathematical Society
- 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