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ON THE FUZZY STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS  

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)
Publication Information
The Pure and Applied Mathematics / v.17, no.1, 2010 , pp. 65-80 More about this Journal
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) = $2a^2 f(x)\;+\;2b^2f(y)$ for nonzero real numbers a, b with $a\;{\neq}\;{\pm}1$.
Keywords
fuzzy Banach space; quadratic functional equation; generalized Hyers-Ulam stability;
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