Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non‐Archimedean Normed Spaces

Abasalt Bodaghi and Sang Og Kim

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: We obtain the general solution of the generalized mixed additive and quadratic functional equation f(x + my) + f(x − my) = 2f(x) − 2m2f(y) + m2f(2y), m is even; f(x + y) + f(x − y) − 2(m2 − 1)f(y) + (m2 − 1)f(2y), m is odd, for a positive integer m. We establish the Hyers‐Ulam stability for these functional equations in non‐Archimedean normed spaces when m is an even positive integer or m = 3.

Date: 2013
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https://doi.org/10.1155/2013/198018

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:198018

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