Let A and B be two unital C∗-algebras with unit I. It is shown that the mapping φ : As →Bs which preserves arithmetic mean and Jordan triple product is a difference of two Jordan homomorphisms provided that 0 ∈ Ranφ. The structure of φ is more refined when φ(I) ≥ 0 or φ(I) ≤ 0. Furthermore, if A is a C∗-algebra of real rank zero and φ : A → B is additive and preserves absolute value of product, then φ = φ1⊕φ2 such that φ1 (respectively, φ2) is a complex linear (respectively, antilinear) ∗-homomorphism.
