Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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ON SOLUTIONS AND STABILITY OF A GENERALIZED QUADRATIC EQUATION ON NON-ARCHIMEDEAN NORMED SPACES

  • 투고 : 2011.10.10
  • 심사 : 2012.03.07
  • 발행 : 2012.09.30
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초록

In this paper we study general solutions and generalized Hyers-Ulam-Rassias stability of the following function equation $$f(x-\sum^{k}_{i=1}x_i)+(k-1)f(x)+(k-1)\sum^{k}_{i=1}(x_i)=f(x-x_1)+\sum^{k}_{i=2}f(x_i-x)+\sum^{k}_{i=1}\sum^{k}_{j=1,j > i}f(x_i+x_j)$$. for $k{\geq}2$, on non-Archimedean Banach spaces. It will be proved that this equation is equivalent to the so-called quadratic functional equation.

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참고문헌

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