In this paper, using fixed point method, we prove the generalized Hyers-Ulam stability of random homomorphisms in random $C^*$-algebras and random Lie $C^*$-algebras and of derivations on Non-Archimedean random C$^*$-algebras and Non-Archimedean random Lie C$^*$-algebras for the following $m$-variable additive functional equation: $$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...
