충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제20권2호
  • /
  • Pages.109-115
  • /
  • 2007
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지

A FUNCTIONAL EQUATION ON HYPERPLANES PASSING THROUGH THE ORIGIN

  • Bae, Jae-Hyeong (Department of Mathematics and Applied Mathematics Kyung Hee University) ;
  • Park, Won-Gil (National Institute for Mathematical Sciences)
  • 투고 : 2007.02.17
  • 발행 : 2007.06.30
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초록

In this paper, we obtain the general solution and the stability of the multi-dimensional Cauchy's functional equation $f(x_1+y_1,{\cdots},x_n+y_n)=f(x_1,{\cdots},x_n)+f(y_1,{\cdots},y_n)$. The function f given by $f(x_1,{\cdots},x_n)=a_1x_1+{\cdots}+a_nx_n$ is a solution of the above functional equation.

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