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Fuzzy approximately cubic mappings. (English) Zbl 1160.46336

Summary: We establish some stability results concerning the cubic functional equation \[ f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x) \] in fuzzy normed spaces. We discuss the fuzzy continuity of the cubic mappings and show that the existence of a solution for any approximately cubic mapping guarantees the completeness of the fuzzy normed space.

MSC:

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