Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지

ON THE STABILITY OF AN n-DIMENSIONAL QUADRATIC EQUATION

  • Jun, Kil-Woung (Department of Mathematics Chungnam National University) ;
  • Lee, Sang-Baek (Department of Mathematics Chungnam National University)
  • Received : 2006.12.27
  • Published : 2007.03.31
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Abstract

Let X and Y be vector spaces. In this paper we prove that a mapping $f:X{\rightarrow}Y$ satisfies the following functional equation $${\large}\sum_{1{\leq}k<l{\leq}n}\;(f(x_k+x_l)+f(x_k-x_l))-2(n-1){\large}\sum_{i=1}^{n}f(x_i)=0$$ if and only if the mapping f is quadratic. In addition we investigate the generalized Hyers-Ulam-Rassias stability problem for the functional equation.

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