Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ON THE STABILITY OF A QUADRATIC FUNCTIONAL EQUATION

  • Lee, Sang-Baek (Department of Mathematics Chungnam National University) ;
  • Han, Mi Hyun (Department of Mathematics Chungnam National University) ;
  • Park, Won-Gil (Department of Mathematics Education Mokwon University)
  • Published : 2012.05.15
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Abstract

In this paper, for any fixed integer $n\;>\;m\;{\geq}\;1$, we investigate the generalized Hyers-Ulam stability of the following quadratic functional equation $f(nx+my)\;+\;f(nx-my)\;=\;mn[f(x+y)\;+\;f(x-y)]\;+\;2(n-m)[nf(x)\;-\;mf(y)]$ in ${p}$-Banach spaces, where $0\;<\;p\;{\leq}\;1$. And we prove the same stability of the above functional equation in 2-Banach spaces.

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References

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