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 \[ |f(x + y) - f(x)f(y)| < \delta \] for some fixed $\delta$ and all x and y in the domain, then f is either bounded or exponential.
D. H. Hyers, On the stability of the linear functional equation, Proc. Mat. Acad. Sci. U.S.A. 27 (1941), 222-224.
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