Homomorphisms and Derivations in $C^*$-Algebras

Abstract

Using the Hyers-Ulam-Rassias stability method of functional equations, we investigate homomorphisms in $C^*$-algebras, Lie $C^*$-algebras, and $JC^*$-algebras, and derivations on $C^*$-algebras, Lie $C^*$-algebras, and $J C^*$-algebras associated with the following Apollonius-type additive functional equation $f (z-x) + f(z-y) + (1/2) f(x+y) = 2f (z- (x+y)/4)$.