fixed point approach to the hyers-ulam-rassias approximation‎ ‎of homomorphisms and derivations on non-archimedean random lie $c^*$-algebras

‎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:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfleft( m x_i‎ + ‎sum_{j=1~,ineq j}^m x_jright)+fleft(sum_{i=1}^m x_iright) right]$$‎ ‎the concept of hyers-ulam-rassias stability originated from th‎. ‎m.‎ ‎rassias� stability theorem that appeared in his paper‎: ‎on the‎ ‎stability of the linear mapping in banach spaces‎, ‎proc‎. ‎amer.‎ ‎math‎. ‎soc‎. ‎72 (1978)‎, ‎297-300.