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A Multidimensional Functional Equation Having Quadratic Forms as Solutions

DOI: 10.1155/2007/24716

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Abstract:

We obtain the general solution and the stability of the m-variable quadratic functional equation f(x1+y1, ¢ € |,xm+ym)+f(x1 ¢ ’y1, ¢ € |,xm ¢ ’ym)=2f(x1, ¢ € |,xm)+2f(y1, ¢ € |,ym). The quadratic form f(x1, ¢ € |,xm)= ¢ ‘1 ¢ ‰ ¤i ¢ ‰ ¤j ¢ ‰ ¤maijxixj is a solution of the given functional equation.

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