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Fuzzy stability of the Jensen functional equation. (English) Zbl 1179.46060

Summary: We establish a generalized Hyers-Ulam-Rassias stability theorem in the fuzzy sense. In particular, we introduce the notion of fuzzy approximate Jensen mapping and prove that, if a fuzzy approximate Jensen mapping is continuous at a point, then we can approximate it by an everywhere continuous Jensen mapping. As a fuzzy version of a theorem of Schwaiger, we also show that if every fuzzy approximate Jensen type mapping from the natural numbers into a fuzzy normed space can be approximated by an additive mapping, then the fuzzy norm is complete.

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
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