Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On the Stability of Orthogonally Cubic Functional Equations

  • Received : 2005.10.31
  • Published : 2007.03.23
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Abstract

Let $f$ denote a mapping from an orthogonality space ($\mathcal{X}$, ${\bot}$) into a real Banach space $\mathcal{Y}$. In this paper, we prove the Hyers-Ulam-Rassias stability of the orthogonally cubic functional equations $f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x)$ and $f(x+y+2z)+f(x+y-2z)+f(2x)+f(2y)=2f(x+y)+4f(x+z)+4f(x-z)+4f(y+z)+4f(y-z)$, where $x{\bot}y$, $y{\bot}z$, $x{\bot}z$.

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