# The $w$-core–EP inverse in rings with involution

## DOI:

https://doi.org/10.33044/revuma.3478## Abstract

The main goal of this paper is to present two new classes of generalized inverses in order to extend the concepts of the (dual) core–EP inverse and the (dual) $w$-core inverse. Precisely, we introduce the $w$-core–EP inverse and its dual for elements of a ring with involution. We characterize the (dual) $w$-core–EP invertible elements and develop several representations of the $w$-core–EP inverse and its dual in terms of different well-known generalized inverses. Using these results, we get new characterizations and expressions for the core–EP inverse and its dual. We apply the dual $w$-core–EP inverse to solve certain operator equations and give their general solution forms.

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