Fuzzy stability of the Jensen functional equation

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.