학술저널
ON THE STABILITY OF AN n-DIMENSIONAL QUADRATIC EQUATION
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 20, No. 1
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2007.0323 - 29 (7 pages)
- 0
Let X and Y be vector spaces. In this paper we prove that a mapping f : X ! Y satis¯es the following functional equa- tion X1·k<l·n(f(xk + xl) + f(xk ¡ xl)) ¡ 2(n ¡ 1)Xni=1f(xi) = 0 if and only if the mapping f is quadratic. In addition we investi-gate the generalized Hyers-Ulam-Rassias stability problem for the functional equation.
1. Introduction
2. Solution of the functional equation (1.2)
3. Stability of the quadratic equation (1.2)
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