Jordan∗-Derivations onC∗-Algebras andJC∗-Algebras

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)‖≤‖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