University of MaraghehSahand Communications in Mathematical Analysis2322-580719420221001Automatic Continuity of Almost $n$-Multiplicative Linear Functionals9710725518010.22130/scma.2022.549567.1065ENAbbasZivari-KazempourDepartment of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.0000-0001-8362-8490Journal Article20220225We 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 $\varphi:A\longrightarrow \mathbb{C}$ is an almost $n$-Jordan homomorphism.https://scma.maragheh.ac.ir/article_255180_2caea4110a982112f722080ec32a3b3d.pdf