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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

$f\left(2x+y\right)+f\left(2x-y\right)=f\left(x+y\right)+f\left(x-y\right)+2f\left(2x\right)-2f\left(x\right)$

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.

##### MSC:
 39B82 Stability, separation, extension, and related topics 39B52 Functional equations for functions with more general domains and/or ranges
##### References:
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