Approximate homomorphisms and derivations in proper JCQ∗JCQ∗-triples via a fixed point method

In this paper, we investigate homomorphisms and derivations in proper JCQ∗JCQ∗-triples with the following functional equation: 1kf(kx+ky+kz)=f(x)+f(y)+f(z) for a fixed positive integer kk. We moreover prove the generalized Hyers–Ulam stability of homomorphisms in proper JCQ∗JCQ∗-triples and of derivations on proper JCQ∗JCQ∗-triples via a fixed point method.