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Stability of a mixed additive, quadratic and cubic functional equation in quasi-Banach spaces. (English) Zbl 1168.39013

The authors consider the following functional equation
\[ f\left(\displaystyle\sum_{j=1}^4 x_j\right)+\displaystyle\sum_{1\leq i< j\leq 4}f(x_i+x_j)=\displaystyle\sum_{i=1}^4 f(x_i)+\displaystyle\sum_{1\leq i< j< k\leq 4}f(x_i+x_j+x_k), \]
deriving from cubic, quadratic and additive functions. They investigate the Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
46B03 Isomorphic theory (including renorming) of Banach spaces
39B52 Functional equations for functions with more general domains and/or ranges
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