HOMOMORPHISMS IN PROPER LIE $CQ^∗$-ALGEBRAS

Abstract

Using the Hyers-Ulam-Rassias stability method of functional equations, we investigate homomorphisms in proper CQ*-algebras and proper Lie CQ*-algebras, and derivations on proper CQ*-algebras and proper Lie CQ*-algebras associated with the following functional equation

\frac{1}{k} f(kx + ky + kz) = f(x) + f(y) + f(z)

for a fixed positive integer k.