Approximately J∗J∗-homomorphisms: A fixed point approach

The functional equation (ξ)(ξ) is stable if any function gg satisfying the equation (ξ)(ξ)approximately   is near to the true solution of (ξ)(ξ). A functional equation is superstable   if every solution satisfying the equation approximately is an exact solution of it. Using fixed point methods, we prove the stability and superstability of J∗J∗-homomorphisms between J∗J∗-algebras for the generalized Jensen-type functional equation f(x+y2)+f(x−y2)=f(x).