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

Abstract

It is proved that if f is a function from a vector space to the real numbers satisfying \[ | f ( x + y ) − f ( x ) f ( y ) | > δ |f(x + y) - f(x)f(y)| > \delta \] for some fixed δ \delta and all x and y in the domain, then f is either bounded or exponential.