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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.17 No.1

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ON THE FUZZY STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS

ON THE FUZZY STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS

한국수학교육학회지시리즈B:순수및응용수학 / 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 (DEPARTMENT OF MATHEMATICS, DAEJIN UNIVERSITY)
Jang, Sun-Young (DEPARTMENT OF MATHEMATICS, UNIVERSITY OF ULSAN)
Shin, Dong-Yun (DEPARTMENT OF MATHEMATICS, UNIVERSITY OF SEOUL)
Lee, Jung-Rye, Jang, Sun-Young, & Shin, Dong-Yun. (2010). ON THE FUZZY STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS. 한국수학교육학회지시리즈B:순수및응용수학, 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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한국수학교육학회지시리즈B:순수및응용수학

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