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Fuzzy almost quadratic functions. (English) Zbl 1157.46048

The authors approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense; this kind of fuzzy normed linear space was introduced by T. Bag and S. K. Samanta [J. Fuzzy Math. 11, 687–705 (2003; Zbl 1045.46048)].
More precisely, they establish a fuzzy Hyers-Ulam-Rassias stability of the quadratic functional equation \(f(x+y)+f(x-y)=2f(x)+2f(y)\). Their result can be regarded as a generalization of the stability phenomenon in the framework of normed linear spaces. They also prove a generalized version of fuzzy stability of the Pexiderized quadratic functional equation \(f(x+y)+f(x-y)=2g(x)+2h(y)\).

MSC:

46S40 Fuzzy functional analysis
39B52 Functional equations for functions with more general domains and/or ranges
39B82 Stability, separation, extension, and related topics for functional equations
26E50 Fuzzy real analysis
46S50 Functional analysis in probabilistic metric linear spaces

Citations:

Zbl 1045.46048
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