Approximate \(n\)-Lie homomorphisms and Jordan \(n\)-Lie homomorphisms on \(n\)-Lie algebras (Q417120)

Summary: 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 \[ \mu f\left(\sum^n_{i=1} x_i/n\right) + \mu \sum^n_{j=2} f\left(\sum^n_{_{\substack{ i=1,\\ i \neq j}}} x_i - (n - 1) x_j/n\right) = f(\mu x_1)\quad(n \geq 2). \]