Fuzzy stability of an additive-quadratic functional equation with the fixed point alternative (Q2791955)

Suppose that \(X\) is a vector space and \((Y, N)\) is a fuzzy Banach space. Let \(n\) be a fixed positive integer and \(f:X\to Y\) be an odd mapping or an even mapping. In this paper, the authors prove the Hyers-Ulam stability of the functional equation NEWLINE\[NEWLINE2nf\left(\frac{1}{2n}\sum_{i=1}^{2n} x_i\right)+\sum_{i=1}^{2n} f\left( x_i-\frac{1}{2n}\sum_{j=1}^{2n} x_j\right)=\sum_{i=1}^{2n}f(x_i)NEWLINE\]NEWLINE by using the fixed point method.