Stability of the Fréchet Equation in Quasi-Banach Spaces

Sang Og Kim
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Sang Og Kim: School of Data Science, Hallym University, Chuncheon 24252, Korea

Mathematics, 2020, vol. 8, issue 4, 1-20

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.

Keywords: Hyers–Ulam stability; hyperstability; Fréchet equation; quasi-Banach space; fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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