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 multiplicative and almost n-multiplicative linear functional on banach algebra a is also investigated. additionally, for commutative banach algebra a, we prove that every almost jordan homomorphism φ : a → c is an almost n-jordan homomorphism.