Approximate a quadratic mapping in multi-Banach spaces, a fixed point approach

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}

Keywords:

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