On the Stability of Quadratic Functional Equations

Jung Rye Lee, Jong Su An and Choonkil Park

Abstract and Applied Analysis, 2008, vol. 2008, issue 1

Abstract: Let X, Y be vector spaces and k a fixed positive integer. It is shown that a mapping f(kx + y) + f(kx-y) = 2k2f(x) + 2f(y) for all x, y ∈ X if and only if the mapping f : X → Y satisfies f(x + y) + f(x-y) = 2f(x) + 2f(y) for all x, y ∈ X. Furthermore, the Hyers‐Ulam‐Rassias stability of the above functional equation in Banach spaces is proven.

Date: 2008
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https://doi.org/10.1155/2008/628178

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2008:y:2008:i:1:n:628178

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