m-Generalized RightWeighted Group Inverse in Banach Algebras

In this paper, we introduce the concept of the m-generalized right w-group inverse. This new inverse naturally extends both the m-weak group inverse and the weak w-group inverse to a more general one-sided setting. We characterize this generalized inverse using the generalized right w-group inverse. We also provide alternative characterizations based on the m-generalized right w-group decomposition and the polar-like property, and investigate the related m-weak right w-group inverse.