Approximate homomorphisms and derivation in multi-Banach algebras

Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in multi-Banach algebras and derivations on multi-Banach algebras for the additive functional equation $$\sum _{i=1}^{m}f(m{x}_i+\sum _{j=1,j\ne i}^m{x}_j)+f\left(\sum _{i=1}^m{x}_i\right)=2f\left(\sum _{i=1}^{m}m{x}_i\right)$$ for each $m\in \mathbb{N}$ with $m\ge 2$.