Jordan ∗‐Derivations on C ∗ ‐Algebras and J C ∗ ‐Algebras

We investigate Jordan ∗‐derivations on C ∗ ‐algebras and Jordan ∗‐derivations on J C ∗ ‐algebras associated with the following functional inequality ∥ f ( x ) + f ( y ) + k f ( z )∥ ≤ ∥ k f (( 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 J C ∗ ‐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.