Stability and hyperstability of orthogonally -m-homomorphisms in orthogonally Lie -algebras: a fixed point approach

摘要

Recently Eshaghi et al. introduced orthogonal sets and proved the real generalization of the Banach fixed point theorem on these sets. In this paper, we prove the real generalization of Diaz-Margolis fixed point theorem on orthogonal sets. By using this fixed point theorem, we study the stability of orthogonally -m-homomorphisms on Lie -algebras associated with the following functional equation: for each . Moreover, we establish the hyperstability of these functional equations by suitable control functions.