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Stability of mixed type cubic and quartic functional equations in random normed spaces. (English) Zbl 1176.39022
Summary: We obtain the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary \(t\)-norms
\[ f(x+2y)+f(x - 2y)=4[f(x+y)+f(x - y)] - 24f(y) - 6f(x)+3f(2y). \]

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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