ISOMORPHISMS AND GENERALIZED DERIVATIONS IN PROPER CQ*-ALGEBRAS

In this paper, we prove the Hyers-Ulam-Rassias stability of homomorphisms in proper CQ*-algebras and of generalized derivations on proper CQ*-algebras for the following Cauchy-Jensen additive mappings: f(x+y+z/2) +f(x−y+z/2)=f(x)+f(z), f(x+y+z/2)−f(x−y+z/2)=f(y),2f(x+y+ z/2)=f(x)+f(y)+f(z), which were introduced and investigated in [3, 30]. This is applied to investigate isomorphisms in proper CQ∗-algebras.