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Stability of pexiderized quadratic functional equation in intuitionistic fuzzy normed space. (English) Zbl 1222.39022

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.

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.

39B82Stability, separation, extension, and related topics
39B52Functional equations for functions with more general domains and/or ranges
46S40Fuzzy functional analysis
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