Stability and superstability of Jordan homomorphisms and Jordan derivations on Banach algebras and C*-algebras: A fixed point approach

Using fixed point methods, we prove the Hyers-Ulam-Rassias stability and superstability of Jordan homomorphisms (Jordan *-homomorphisms), and Jordan derivations (Jordan *-derivations) on Banach algebras (C*-algebras) for the generalized Jensen-type functional equation rf(x+yr)+rf(x-yr)=2f(x), where r is a fixed positive real number in (1,∞).