Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ADDITIVE-QUARTIC FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN ORTHOGONALITY SPACES

  • Received : 2011.12.16
  • Accepted : 2012.01.15
  • Published : 2012.03.30
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Abstract

Using the direct method, we prove the Hyers-Ulam stability of the orthogonally additive-quartic functional equation (0.1) $f(2x+y)+f(2x-y)=4f(x+y)+4f(x-y)+10f(x)+14f(-x)-3f(y)-3f(-y)$ for all $x$, $y$ with $x{\perp}y$, in non-Archimedean Banach spaces. Here ${\perp}$ is the orthogonality in the sense of R$\ddot{a}$tz.

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References

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