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Stability of Cubic and Quartic Functional Equations in Non-Archimedean Spaces

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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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Authors and Affiliations

  1. Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran

    M. Eshaghi Gordji & M. B. Savadkouhi

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  1. M. Eshaghi Gordji
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  2. M. B. Savadkouhi
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Correspondence to M. Eshaghi Gordji.

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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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