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On Stability of a Functional Equation Connected with the Reynolds Operator

Abstract

Let be an Abelain semigroup,, and let be either or. We prove superstability of the functional equation in the class of functions. We also show some stability results of the equation in the class of functions.

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References

  1. Hyers DH, Isac G, Rassias ThM: Stability of Functional Equations in Several Variables, Progress in Nonlinear Differential Equations and Their Applications. Volume 34. Birkhäuser Boston, Boston, Mass, USA; 1998:vi+313.

    Google Scholar 

  2. Aczél J, Dhombres J: Functional Equations in Several Variables, Encyclopedia of Mathematics and Its Applications. Volume 31. Cambridge University Press, Cambridge, UK; 1989:xiv+462.

    Book  Google Scholar 

  3. Dubreil-Jacotin M-L: Propriétés algébriques des transformations de Reynolds. Comptes Rendus de l'Académie des Sciences 1953, 236: 1950–1951.

    MathSciNet  MATH  Google Scholar 

  4. Matras Y: Sur l'équation fonctionnelle. Académie Royale de Belgique. Bulletin de la Classe des Sciences. 5e Série 1969, 55: 731–751.

    MathSciNet  MATH  Google Scholar 

  5. Ger R, Šemrl P: The stability of the exponential equation. Proceedings of the American Mathematical Society 1996,124(3):779–787. 10.1090/S0002-9939-96-03031-6

    Article  MathSciNet  MATH  Google Scholar 

  6. Baker JA, Lawrence J, Zorzitto F: The stability of the equation. Proceedings of the American Mathematical Society 1979,74(2):242–246.

    MathSciNet  MATH  Google Scholar 

  7. Baker JA: The stability of the cosine equation. Proceedings of the American Mathematical Society 1980,80(3):411–416. 10.1090/S0002-9939-1980-0580995-3

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Adam Najdecki.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Najdecki, A. On Stability of a Functional Equation Connected with the Reynolds Operator. J Inequal Appl 2007, 079816 (2007). https://doi.org/10.1155/2007/79816

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