Homomorphisms and derivations in proper JCQ∗-triples

In this paper, we investigate homomorphisms in proper JCQ∗-triples and derivations on proper JCQ∗-triples associated with the following functional equation 1 k f (kx +ky +kz) = f (x)+ f (y) +f (z) for a fixed positive integer k. We moreover prove the generalized Hyers–Ulam stability of homomorphisms in proper JCQ∗-triples and of derivations on proper JCQ∗-triples. This is applied to investigate isomorphisms between proper JCQ∗-triples. © 2007 Elsevier Inc. All rights reserved