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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. Zbigniew Gajda, 1991. "On stability of additive mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-4, January.
    2. 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.
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