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Stability of the Fréchet Equation in Quasi-Banach Spaces

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  • Sang Og Kim

    (School of Data Science, Hallym University, Chuncheon 24252, Korea)

Abstract

We investigate the Hyers–Ulam stability of the well-known Fréchet functional equation that comes from a characterization of inner product spaces. We also show its hyperstability on a restricted domain. We work in the framework of quasi-Banach spaces. In the proof, a fixed point theorem due to Dung and Hang, which is an extension of a fixed point theorem in Banach spaces, plays a main role.

Suggested Citation

  • Sang Og Kim, 2020. "Stability of the Fréchet Equation in Quasi-Banach Spaces," Mathematics, MDPI, vol. 8(4), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:490-:d:340079
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    References listed on IDEAS

    as
    1. Gwang Hui Kim, 2001. "On the stability of the quadratic mapping in normed spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 25, pages 1-13, January.
    2. Zbigniew Gajda, 1991. "On stability of additive mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-4, January.
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