Using the fixed point method, we prove some results concerning the stability of the functional equation \[ um_{i=1}^{2n}f\bigg(x_i-\frac1{2n}um_{j=1}^{2n}x_j\bigg)=um_{i=1}^{2n}f(x_i)-2nf\bigg(\frac1{2n}um_{i=1}^{2n}x_i\bigg) \] where $f$ is defined on a vector space and taking values in a fuzzy Banach space, which is said to be a functional equation related to a characterization of inner product spaces.