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Zbl 1222.39022
Mohiuddine, S.A.; Şevli, H.
Stability of pexiderized quadratic functional equation in intuitionistic fuzzy normed space.
(English)
[J] J. Comput. Appl. Math. 235, No. 8, 2137-2146 (2011). ISSN 0377-0427

The authors consider the Pexider form $f(x+y)+f(x-y)=2g(x)+2h(y)$ of the quadratic functional equation and investigate the stability thereof in the case of intuitionistic fuzzy normed Banach spaces under certain additional conditions.\par It should be remarked that the definition of Cauchy sequences given at the very beginning seems to be incorrect. Transformed to classical'' normed spaces the definition would mean that a sequence $(x_n)$ is Cauchy if $x_{n+p}-x_n$ tended to zero for $n$ to infinity for all (fixed) $p$. The sequence of the numbers $\ln(n)$ obviously satisfies the above condition, is unbounded, and thus not a Cauchy sequence.
[Jens Schwaiger (Graz)]
MSC 2000:
*39B82 Stability, separation, extension, and related topics
39B52 Functional equations for functions with more general domains
46S40 Fuzzy functional analysis

Keywords: $t$-norm; $t$-conorm; intuitionistic fuzzy normed space; pexiderized quadratic functional equation; Hyers-Ulam-Rassias stability

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