Definition:Cauchy Functional Equation
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Definition
Let $f: \R \to \R$ be a real function.
Then the Cauchy functional equation is:
- $\forall x, y \in \R: \map f {x + y} = \map f x + \map f y$
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Also see
- The fifth problem on Hilbert's list is a generalisation of this equation.
- Definition:Additive Function (Conventional): a real function that satisfies this equation
Source of Name
This entry was named for Augustin Louis Cauchy.