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

John Baker, J. Lawrence, F. Zorzitto

Source record

Source: Crossref

Published: May 1, 1979

DOI: 10.1090/s0002-9939-1979-0524294-6

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Source 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.

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The stability of the equation 𝑓(𝑥+𝑦)=𝑓(𝑥)𝑓(𝑦) — Mathematical Frontier Network