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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.

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  • [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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Keywords: Functional equation, stability
Article copyright: © Copyright 1990 American Mathematical Society

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