Hybrid core-EP-(b,c)- inverse in rings

In this paper, we study when the core inverse in a ring coincides with its hybrid $(b,c)$-inverse, i.e., hybrid core-$(b,c)$-inverse. We present many characterizations of hybrid core-$(b,c)$-inverse. To establish a broader framework for this generalized inverses, we define hybrid core-EP-$(b,c)$-inverse that serves as a natural extension of the hybrid core-$(b,c)$-inverse. We characterize this new generalized inverse by combining the hybrid core-$(b,c)$-inverses and quasinilpotents. This generalized inverse is thereby examined through a novel limit-based approach. Its polar-like properties and image-based representations are presented.