Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A FUNCTIONAL EQUATION RELATED TO HYPERPLANES

  • Park, Won-Gil (National Institute for Mathematical Sciences) ;
  • Bae, Jae-Hyeong (Department of Mathematics and Applied Mathematics, Kyung Hee University)
  • Published : 2007.05.31

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Abstract

In this paper, we obtain the general solution and the stability of the multi-dimensional Jensen's functional equation $$2f(\frac{x_1+y_1}{2},\;\cdots,\;\frac{x_n+y_n}{2})=f(x_1,\;\cdots,\;x_n)+f(y_1,\;\cdots,\;y_n)$$. The function f given by $f(x_1,\;\cdots,\;x_n)=a_1x_1+{\cdots}+a_nx_n+b$ is a solution of the above functional equation.

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