Approximately n-Jordan Homomorphisms on Banach Algebras.

Let n ϵ N, and let A, B be two rings. An additive map h : A → B is called n-Jordan homomorphism if h(a_n) = (h(a))ⁿ for all a ϵ A. In this paper, we establish the Hyers-Ulam-Rassias stability of n-Jordan homomorphisms on Banach algebras. Also we show that (a) to each approximate 3-Jordan homomorphism h from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique 3-ring homomorphism near to f, (b) to each approximate n-Jordan homomorphism h between two commutative Banach algebras there corresponds a unique n-ring homomorphism near to f for all n ϵ (3, 4, 5). [ABSTRACT FROM AUTHOR]