University of MaraghehSahand Communications in Mathematical Analysis2322-580718220210501Joint Continuity of Bi-multiplicative Functionals334424086110.22130/scma.2020.127223.795ENAbbasZivari-KazempourDepartment of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.MohamadValaeiDepartment of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.Journal Article20200507For Banach algebras $mathcal{A}$ and $mathcal{B}$, we show that if $mathfrak{A}=mathcal{A}times mathcal{B}$ is unital, then each bi-multiplicative mapping from $mathfrak{A}$ into a semisimple commutative Banach algebra $mathcal{D}$ is jointly continuous. This conclusion generalizes a famous result due to<br />$check{text{S}}$ilov, concerning the automatic continuity of homomorphisms between Banach algebras. We also prove that every $n$-bi-multiplicative functionals on $mathfrak{A}$ is continuous if and only if it is continuous for the case $n=2$. https://scma.maragheh.ac.ir/article_240861_e6375ff83f49e906b56ffeaaf06256ae.pdf