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Quadratic-quartic functional equations in RN-spaces. (English) Zbl 1187.39036
Summary: We obtain the general solution and the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary \(t\)-norms
\[ f(2x+y)+f(2x - y)=4[f(x+y)+f(x - y)]+2[f(2x) - 4f(x)] - 6f(y). \]

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
46B09 Probabilistic methods in Banach space theory
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