Document Type : Original Article
1 Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
2 Department of Mathematics, Payame Noor University, P.O. Box. 19395-3697, Tehran, Iran
3 Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran
In this paper, we introduce the notion of b-Banach spaces and we present some examples. Also, we give an important extension of the Hahn-Banach theorem in a $b$-Banach space with an application.