Proposition: Functional Equation of the Exponential Function of General Base (Revised)

Let \(f:\mathbb R\to \mathbb R\) be any continuous real function that obeys the functional equation

\[f(x+y)=f(x)\cdot f(y)\]

for all \(x,y\in\mathbb R\). Then there are two possible cases:

Proofs: 1

Proofs: 1


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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983