Isomorphisms and derivations in C*-Algebras

In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality: equation(0.1)∥f(x)+f(y)+2f(z)+2f(w)∥≤‖2|f(x+y2+z+w)‖This is applied to investigate isomorphisms between C*-algebras, Lie C*-algebras and JC*-algebras, and derivations on C*-algebras, Lie C*-algebras and JC*-algebras, associated with the Cauchy-Jensen functional equation 2f(x+y2+z+w)=f(x)+f(y)+2f(z)+2f(w).