Stability of cubic and quartic functional equations in non-Archimedean spaces

Details Stability of cubic and quartic functional equations in non-Archimedean spaces Stability of cubic and quartic functional equations in non-Archimedean spaces

2008-12-30

arxiv.org/abs/0812.5015v1

Mathematics

Functional Analysis

Scientific paper

We prove generalized Hyres-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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