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The Best Ulam Constant of the Fréchet Functional Equation

Author

Listed:
  • Irina Opraie

    (Department of Mathematics, Technical University of Cluj-Napoca, G. Bariţiu No. 25, 400027 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

  • Dorian Popa

    (Department of Mathematics, Technical University of Cluj-Napoca, G. Bariţiu No. 25, 400027 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

  • Liana Timboş

    (Department of Mathematics, Technical University of Cluj-Napoca, G. Bariţiu No. 25, 400027 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

Abstract

In this paper, we prove the Ulam stability of the Fréchet functional equation f ( x + y + z ) + f ( x ) + f ( y ) + f ( z ) = f ( x + y ) + f ( y + z ) + f ( z + x ) arising from the characterization of inner product spaces and we determine its best Ulam constant. Using this result, we give a stability result for a pexiderized version of the Fréchet functional equation.

Suggested Citation

  • Irina Opraie & Dorian Popa & Liana Timboş, 2022. "The Best Ulam Constant of the Fréchet Functional Equation," Mathematics, MDPI, vol. 10(10), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1769-:d:821335
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    References listed on IDEAS

    as
    1. Anderson, Douglas R. & Onitsuka, Masakazu, 2019. "Hyers–Ulam stability for a discrete time scale with two step sizes," Applied Mathematics and Computation, Elsevier, vol. 344, pages 128-140.
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