RGNNA Publishing Group.Mathematical Analysis and its Contemporary Applications2716-98983320210901A new version of the Hahn Banach theorem in b-Banach spaces273268327710.30495/maca.2021.1929965.1011ENMohammad RezaHaddadiDepartment of Mathematics, Ayatollah Boroujerdi University, Boroujerd, IranHosseinAlaeidizajiDepartment of Mathematics, Payame Noor University, P.O. Box. 19395-3697, Tehran, IranVahidParvanehDepartment of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, IranJournal Article20210507In 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.https://www.macajournal.com/article_683277_e52ef706cb1063158527a9ebec809845.pdf