Automatic Continuity of Almost n-Multiplicative Linear Functionals

We generalize a theorem due to Jarosz, by proving that every almost n-multiplicative linear functional on Banach algebra A is automatically continuous. The relation between almost mul- tiplicative and almost n-multiplicative linear functional on Banach algebra A is also investigated. Additionally, for commutative Ba- nach algebra A, we prove that every almost Jordan homomorphism φ : A −→ C is an almost n-Jordan homomorphism.