Abstract
We introduce new classes of generalized Drazin inverses in a ring, which are called the generalized n-strong Drazin inverse and pseudo n-strong Drazin inverse for arbitrary . Some basic properties of these inverses are studied. We prove extensions of Cline's formula for these inverses and Jacobson's lemma for generalized and pseudo strong Drazin inverse. In a Banach algebra, we define and characterize the weighted generalized strong Drazin inverse and weighted pseudo strong Drazin inverse.
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Acknowledgments
The author is grateful to referees for constructive comments and careful reading of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.