Abstract
We prove generalized Hyers-Ulam–Rassias stability of the cubic functional equation f(kx+y)+f(kx−y)=k[f(x+y)+f(x−y)]+2(k 3−k)f(x) for all \(k\in \Bbb{N}\) and the quartic functional equation f(kx+y)+f(kx−y)=k 2[f(x+y)+f(x−y)]+2k 2(k 2−1)f(x)−2(k 2−1)f(y) for all \(k\in \Bbb{N}\) in non-Archimedean normed spaces.
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Eshaghi Gordji, M., Savadkouhi, M.B. Stability of Cubic and Quartic Functional Equations in Non-Archimedean Spaces. Acta Appl Math 110, 1321–1329 (2010). https://doi.org/10.1007/s10440-009-9512-7
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DOI: https://doi.org/10.1007/s10440-009-9512-7
Keywords
- Generalized Hyers–Ulam–Rassias stability
- Cubic functional equation
- Quartic functional equation
- Non-Archimedean space
- p-adic