On generalized n-strong Drazin-\(\mathcal {R}\) inverses in Banach algebras

Inspired by Mosić (Linear Multilinear Algebra 69(2):361–375, 2021) and Živković-Zlatanović (Linear Multilinear Algebra, 2023. https://doi.org/10.1080/03081087.2023.2181940), this paper aims to introduce generalized n-strong Drazin- \(\mathcal {R}\) $\mathcal{R}$ invertible elements. Several characterizations are given to detect the so called generalized n-strong Drazin- \(\mathcal {R}\) $\mathcal{R}$ invertible elements. Also, we extend the Cline’s formula to the context of generalized Drazin- \(\mathcal {R}\) $\mathcal{R}$ (resp. generalized n-strong Drazin- \(\mathcal {R}\) $\mathcal{R}$ ) invertible elements.