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http://dx.doi.org/10.14403/jcms.2012.25.2.171

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)
Publication Information
Journal of the Chungcheong Mathematical Society / v.25, no.2, 2012 , pp. 171-182 More about this Journal
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.
Keywords
Hyers-Ulam stability; quadratic functional equation; p- Banach space;
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