The stability of the cosine equation

Baker, John A.

doi:10.1090/S0002-9939-1980-0580995-3

The stability of the cosine equation
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by John A. Baker

Proc. Amer. Math. Soc. 80 (1980), 411-416

DOI: https://doi.org/10.1090/S0002-9939-1980-0580995-3

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Abstract:

If $\delta > 0$, G is an abelian group and f is a complex-valued function defined on G such that $|f(x + y) + f(x - y) - 2f(x)f(y)| \leqslant \delta$ for all $x,y \in G$, then either $|f(x)| \leqslant (1 + \sqrt {1 + 2\delta } )/2$ for all $x \in G$ or $f(x + y) + f(x - y) = 2f(x)f(y)$ for all $x,y \in G$.

References

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