Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 39B70, 39B20

Retrieve articles in all journals with MSC: 39B70, 39B20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0580995-3
PII: S 0002-9939(1980)0580995-3
Keywords: Functional equation, cosine equation, stability
Article copyright: © Copyright 1980 American Mathematical Society