HOMOMORPHISMS IN PROPER LIE CQ*-ALGEBRAS

Abstract

Using the Hyers-Ulam-Rassias stability method of functional equations, we investigate homomorphisms in proper <TEX>$CQ^*$</TEX>-algebras and proper Lie <TEX>$CQ^*$</TEX>-algebras, and derivations on proper <TEX>$CQ^*$</TEX>-algebras and proper Lie <TEX>$CQ^*$</TEX>-algebras associated with the following functional equation <TEX>$$\frac{1}{k}f(kx+ky+kz)=f(x)+f(y)+f(z)$$</TEX> for a fixed positive integer <TEX>$k$</TEX>.