Approximate n -Lie Homomorphisms and Jordan n -Lie Homomorphisms on n -Lie Algebras

Abstract

Using fixed point methods, we establish the stability of $n$-Lie homomorphisms and Jordan $n$-Lie homomorphisms on $n$-Lie algebras associated to the following generalized Jensen functional equation $\mu f({\sum }_{i=1}^n{x}_i/n)+\mu {\sum }_{j=2}^{n}f({\sum }_{i=1,i\ne j}^n{x}_i-(n-1)x_j/n)=f\left(\mu x_1\right)(n\ge 2)$.