تقریب هایرز –اولام-راسیاس همومورفیسمها و مشتقات در فضاهای غیرارشمیدسی تصادفی جبرهای لی

‎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.

Keywords:

Additive functional equation‎ , ‎fixed point‎ , ‎Non-Archimedean random space‎ , ‎homomorphism‎ ‎in $C^*$-algebras and Lie $C^*$-algebras , ‎ ‎generalized Hyers-Ulam stability‎ , ‎derivation on $C^*$-algebras and Lie $C^*$-algebras