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 JC*- algebras associated with the following Apollonius-type additive functional equation f ( z- x)+ f ( z- y) + ( 1/ 2) f ( x + y) = 2 f ( z-( x + y)/ 4).