Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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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)
  • Received : 2007.02.17
  • Published : 2007.06.30
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Abstract

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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