On approximate n-Jordan homomorphisms - Gselmann, Eszter (Annales Mathematicae Silesianae, 2014)
The aim of this paper it to characterize n-Jordan homomorphisms and to investigate their connection with n-homomorphisms as well as homomorphisms. Furthermore, the following implication is also verified: if a function ϕ is additive and (for a fixed integer n≥2) the mapping x ↦ ϕ(xn)-ϕ(x)n satisfies some mild regularity assumption, then the function ϕ is an n-homomorphism or it is a continuous additive function.