Fuzzy stability of a functional equation associated with inner product spaces
Using some ideas of \textit{A. K. Mirmostafaee} and \textit{M. S. Moslehian} [Fuzzy Sets Syst. 159, No.~6, 720--729 (2008; Zbl 1178.46075)], the author proves the generalized Hyers-Ulam stability of the functional equation \[ 2f\left(\frac{x+y}{2}\right)+f\left(\frac{x-y}{2}\right)+f\left(\frac{y-x}{2}\right)=f(x)+f(y) \] in fuzzy Banach spaces for odd and even cases. This functional equation is related to a characterization of inner product spaces; see \textit{M. S. Moslehian} [Linear Algebra Appl. 429, No.~8--9, 2159--2167 (2008; Zbl 1156.47021)].
scientific article; zbMATH DE number 5634462
scientific article