Biswas, R.Roy, F.2026-02-032025Indian Journal of Pure and Applied Mathematics, 2025, 56, 3, pp. 917-929195588https://doi.org/10.1007/s13226-025-00811-8https://idr.nitk.ac.in/handle/123456789/20108In this paper, we establish some necessary and sufficient conditions for generalized n-strong Drazin invertibility (gns-invertibility) and pseudo n-strong Drazin invertibility (pns-invertibility) of an element in a Banach algebra for n?N. Subsequently, these results are utilized to prove some additive properties of gns (pns)-Drazin inverse. This process produces a generalization of some recent results of H Chen, M Sheibani (Linear and Multilinear Algebra 70.1 (2022): 53-65) for gns and pns-Drazin inverse. © The Indian National Science Academy 2025.Additive propertygns-Drazin inverseJacobson radicalpns-Drazin inverse