Approximately n--Jordan derivations: A fixed point approach

Abstract

Let $n\in \mathbb{N}-\{1\},$ and let $A$ be a Banach algebra. An additive map $D:A\to A$ is called n-Jordan derivation if $$D(a^n)=D(a)a^{n-1}+aD(a)a^{n-2}+...+a^{n-2}D(a)a+a^{n-1}D(a),$$ for all $a\in A$. Using fixed point methods, we investigate the stability of n--Jordan derivations (n--Jordan ${}^{\ast }-$derivations) on Banach algebras ($C^{\ast }-$algebras). Also we show that to each approximate ${}^{\ast }-$Jordan derivation $f$ in a $C^{\ast }-$ algebra there corresponds a unique ${}^{\ast }-$derivation near to $f$.

References in corpus (1)

• On approximate n-ring homomorphisms and n-ring derivations