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 ∑𝜇𝑓(𝑛𝑖=1𝑥𝑖∑/𝑛)+𝜇𝑛𝑗=2∑𝑓(𝑛𝑖=1,𝑖≠𝑗𝑥𝑖−(𝑛−1)𝑥𝑗/𝑛)=𝑓(𝜇𝑥1)(𝑛≥2).