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Stability of the Apollonius Type Additive Functional Equation in Modular Spaces and Fuzzy Banach Spaces
Open AccessArticle

Stability of the Fréchet Equation in Quasi-Banach Spaces

School of Data Science, Hallym University, Chuncheon 24252, Korea
Mathematics 2020, 8(4), 490; https://doi.org/10.3390/math8040490
Received: 24 February 2020 / Revised: 24 March 2020 / Accepted: 24 March 2020 / Published: 1 April 2020
(This article belongs to the Special Issue Functional Inequalities and Equations)
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. View Full-Text
Keywords: Hyers–Ulam stability; hyperstability; Fréchet equation; quasi-Banach space; fixed point theorem Hyers–Ulam stability; hyperstability; Fréchet equation; quasi-Banach space; fixed point theorem
MDPI and ACS Style

Kim, S.O. Stability of the Fréchet Equation in Quasi-Banach Spaces. Mathematics 2020, 8, 490.

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