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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


The stability of the cosine equation

Author: John A. Baker
Journal: Proc. Amer. Math. Soc. 80 (1980), 411-416
MSC: Primary 39B70; Secondary 39B20
MathSciNet review: 580995
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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 $ \vert f(x + y) + f(x - y) - 2f(x)f(y)\vert \leqslant \delta $ for all $ x,y \in G$, then either $ \vert f(x)\vert \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$.

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Additional Information

PII: S 0002-9939(1980)0580995-3
Keywords: Functional equation, cosine equation, stability
Article copyright: © Copyright 1980 American Mathematical Society

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