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Zbl 1192.39018
Eshaghi Gordji, M.; Bavand Savadkouhi, M.
Stability of cubic and quartic functional equations in non-Archimedean spaces.
(English)
[J] Acta Appl. Math. 110, No. 3, 1321-1329 (2010). ISSN 0167-8019; ISSN 1572-9036/e

Using some ideas of {\it M. S. Moslehian} and {\it Th. M. Rassias} [Appl. Anal. Discrete Math. 1, No.~2, 325--334 (2007; Zbl 1257.39019)], {\it K. W. Jun} and {\it H. M. Kim} [J. Math. Anal. Appl. 274, No.~2, 867--878 (2002; Zbl 1021.39014)] and {\it W. G. Park} and {\it J. H. Bae} [Nonlinear Anal., Theory Methods Appl. 62, No.~4 (A), 643--654 (2005; Zbl 1076.39027)], the authors investigate the generalized Hyers-Ulam-Rassias stability of the cubic functional equation $$f(kx+y)+f(kx-y)=k[f(x+y)+f(x-y)]+2(k^3-k)f(x),$$ 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 $k\in \mathbb N$, where $f:G\to X$ is a mapping, $G$ is an additive group and $X$ is a complete non-Archimedean space.
MSC 2000:
*39B82 Stability, separation, extension, and related topics
46S10 Functional analysis over fields (not R, C, or quaternions)
39B52 Functional equations for functions with more general domains

Keywords: generalized Hyers-Ulam-Rassias stability; cubic functional equation; quartic functional equation; non-Archimedean space; p-adic; additive group

Citations: Zbl 1021.39014; Zbl 1076.39027; Zbl 1257.39019

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