Jordan *-derivations on \(C^*\)-algebras and \(JC^*\)-algebras (Q1008561)

Summary: We investigate Jordan *-derivations on \(C^*\)-algebras and Jordan *-derivations on \(JC^*\)-algebras associated with the following functional inequality \(\| f(x)+f(y)+kf(z)\| \leq \| kf((x+y)/k+z)\| \) for some integer \(k\) greater than 1. We moreover prove the generalized Hyers-Ulam stability of Jordan *-derivations on \(C^*\)-algebras and of Jordan *-derivations on \(JC^*\)-algebras associated with the following functional equation \(f((x+y)/k+z)=(f(x)+f(y))/k+f(z)\) for some integer \(k\) greater than 1.