Approximately Multiplicative Mappings. Superstability
The stability of the functional equation f (x + y) = f (x) f (y) was studied by J. Baker, J. Lawrence and F. Zorzitto (1979). They proved that if f is a function from a real vector space W to the real numbers satisfying |f (x+y) -f (x) f (y) | < δ for some fixed δ> 0 and all x, y in W, then f is either bounded or else f (x + y) = f (x)f (y) for all x,y in W.
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