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 $J{C}^{*}$-algebras, and derivations on $C^{*}$-algebras, Lie $C^{*}$-algebras, and $J{C}^{*}$-algebras associated with the following Apollonius-type additive functional equation $f\left(z-x\right)+f\left(z-y\right)+\left(1/2\right)f\left(x+y\right)=2f\left(z-\left(x+y\right)/4\right)$.