Fixed point approach to the Hyers-Ulam-Rassias approximation‎ ‎of homomorphisms and derivations on Non-Archimedean random Lie $C^*$-algebras

Document Type: Research articles


Department of Mathematics, Beyza Branch, Islamic Azad University, Beyza, Iran.


‎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.