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

Abstract

We investigate Jordan $\ast$-derivations on $C^{\ast }$-algebras and Jordan $\ast$-derivations on $J{C}^{\ast }$-algebras associated with the following functional inequality $\Vert f\left(x\right)+f\left(y\right)+kf\left(z\right)\Vert \le \Vert kf\left(\left(x+y\right)/k+z\right)\Vert$ for some integer $k$ greater than 1. We moreover prove the generalized Hyers-Ulam stability of Jordan $\ast$-derivations on $C^{\ast }$-algebras and of Jordan $\ast$-derivations on $J{C}^{\ast }$-algebras associated with the following functional equation $f\left(\left(x+y\right)/k+z\right)=\left(f\left(x\right)+f\left(y\right)\right)/k+f\left(z\right)$ for some integer $k$ greater than 1.