Homomorphisms between C*-algebras associated with the trif functional equation and linear derivations on C*-algebras

It is shown that every almost linear mapping h: A --> 8 of a unital C*-algebra A to a unital C*-algebra B is a homomorphism under some condition on multiplication, and that every almost linear continuous mapping h : A --> B of a unital C*-algebra A of real rank zero to a unital C*-algebra 8 is a homomorphism under some condition on multiplication. Furthermore, we are going to prove the generalized Hyers-Ulam-Rassias stability of *-homomorphisms between unital C*-algebras, and of C-linear *-derivations on unital C*-algebras.