Let 𝒜 and ℬ be Banach algebras and let φ:𝒜→ℬ be a Jordan homomorphism. We show that, under special hypotheses, φ is ring homomorphism. Some related results are given as well.

In this paper, we give the general solution of the Euler–Lagrange–Rassias-type quadratic functional equation [Formula: see text] and investigate its generalized Hyers–Ulam stability.

We prove that each surjective Jordan homomorphism from a Banach algebra [Formula: see text] onto a semiprime commutative Banach algebra [Formula: see text] is a homomorphism, and each 5-Jordan homomorphism from a unital Banach algebra [Formula: see text] into a semisimple commutative Banach algebra [Formula: see text] is a 5-homomorphism.

We show that, under special hypotheses, each 3-Jordan homomorphism ${\it\varphi}$ between Banach algebras ${\mathcal{A}}$ and ${\mathcal{B}}$ is a 3-homomorphism.

No abstract