The fixed point method for fuzzy stability of the Jensen functional equation (Q1037972)

The Jensen functional equation is \[ 2f\left(\frac{x+y}{2}\right) = f(x) + f(y) \] where the unknown \(f\) is a mapping between linear spaces. In this paper, however, the unknown is considered as a mapping between fuzzy-normed linear spaces. The author comes up with an alternative proof and a slight improvement of a recently obtained generalized Hyers-Ulam-Rassias stability of such Jensen equation [\textit{A. K. Mirmostafaee, M. Mirzavaziri} and \textit{M. S. Moslehian}, ``Fuzzy stability of the Jensen functional equation'', Fuzzy Sets Syst. 159, No. 6, 730--738 (2008; Zbl 1179.46060)]. The proof is based, besides several ideas of the original approach, on the fixed-point theory for the probabilistic metric spaces.