n-Jordan homomorphisms

Abstract

Let $n\in \mathbb{N},$ and let $A,B$ be two rings. An additive map $h:A\to B$ is called n-Jordan homomorphism if $h(a^n)=(h(a){)}^n$ for all $a\in A$. Every Jordan homomorphism is an n-Jordan homomorphism, for all $n\ge 2,$ but the converse is false, in general. In this paper we investigate the n-Jordan homomorphisms on Banach algebras. Indeed some results related to continuity are given as well.