Extension of the pseudo Drazin inverse in Banach algebras

In this paper, we study a new class of generalized inverses in Banach algebras, which is termed extended pseudo Drazin inverse. We derive several characterizations and elementary properties of the extended pseudo Drazin inverse. Moreover, we obtain the generalized versions of Jacobson?s lemma for extended Drazin inverse, extended generalized Drazin inverse and extended pseudo Drazin inverse.