- - - Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran
- - - Department of Mathematics, Sahand University of Technology, Tabriz, Iran

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces:\begin{equation}\sum_{ j = ۱}^{n}f\Big(-۲ x_{j} + \sum_{ i = ۱, \neq j}^{n} x_{i}\Big) =(n-۶) f\Big(\sum_{ i = ۱}^{n} x_{i}\Big) + ۹ \sum_{ i = ۱}^{n}f(x_{i}).\end{equation}

Fixed point method, Hyers-Ulam-Rassias stability, Multi-Banach spaces, Quadratic mapping