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Stability of a functional equation deriving from quadratic and additive functions in quasi-banach spaces. (English) Zbl 1127.39055
The authors establish the general solution of the functional equation \[ f(2x+y)+f(2x-y)=f(x+y)+f(x-y)+2f(2x)-2f(x) \] deriving from quadratic and additive functions. They also prove the Hyers-Ulam-Rassias stability for the above equation in quasi Banach spaces.
The authors missed citing the paper by J. Tabor [Ann. Pol. Math. 83, No. 3, 243–255 (2004; Zbl 1101.39021)], which contains the first result about the stability of quasi-Banach spaces.

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
Full Text: DOI
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