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  • P-ISSN1226-0657
  • E-ISSN2287-6081
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ISSN : 1226-0657

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Vol.17 No.1

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ON THE FUZZY STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2010, v.17 no.1, pp.65-80
Lee, Jung-Rye
Jang, Sun-Young
Shin, Dong-Yun
Lee,, J. , Jang,, S. , & Shin,, D. (2010). ON THE FUZZY STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 17(1), 65-80.

Abstract

In [17, 18], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations in fuzzy Banach spaces: (0.1) f(x + y) + f(x - y) = 2f(x) + 2f(y), (0.2) f(ax + by) + f(ax - by) = <TEX>$2a^2 f(x)\;+\;2b^2f(y)$</TEX> for nonzero real numbers a, b with <TEX>$a\;{\neq}\;{\pm}1$</TEX>.

keywords
fuzzy Banach space, quadratic functional equation, generalized Hyers-Ulam stability

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