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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 sine and cosine functional equations


Author: László Székelyhidi
Journal: Proc. Amer. Math. Soc. 110 (1990), 109-115
MSC: Primary 39B50
MathSciNet review: 1015685
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Abstract: In this work the stability of the functional equations describing the addition theorems for sine and cosine is proved.


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

  • [1] J. A. Baker, J. Lawrence, and F. Zorzitto, The stability of the equation $ f\left( {x + y} \right) = f\left( x \right)f\left( y \right)$, Proc. Amer. Math. Soc. 74 (1979), 242-246. MR 524294 (80d:39009)
  • [2] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224. MR 0004076 (2:315a)
  • [3] L. Székelyhidi, On a theorem of Baker, Lawrence, and Zorzitto, Proc. Amer. Math. Soc. 84 (1982), 95-96. MR 633285 (83a:39011)
  • [4] -, Fréchet equation and Hyers's theorem on noncommutative semigroups, Ann. Polon. Math. 48 (1988), 183-189. MR 960000 (89j:39013)
  • [5] -, An abstract superstability theorem, Abhandl. Math. Sem. Univ. Hamburg. (to appear).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1015685-2
PII: S 0002-9939(1990)1015685-2
Keywords: Functional equation, stability
Article copyright: © Copyright 1990 American Mathematical Society